simplicity and superrigidity of twin building lattices kac moody groups over finite fields are finitely generated groups most of them can naturally be viewed as irreducible lattices in products of two closed automorphism groups of non positively curved twinned buildings those are the most important but not the only examples of twin building lattices we prove that these lattices are simple if the corresponding buildings are irreducible and not of affine type i e they are not bruhat tits buildings many of them are finitely presented and enjoy property t our arguments explain geometrically why simplicity fails to hold only for affine kac moody groups moreover we prove that a nontrivial continuous homomorphism from a completed kac moody group is always proper we also show that kac moody lattices fulfill conditions implying strong superrigidity properties for isometric actions on non positively curved metric spaces most results apply to the general class of twin building lattices

the asymptotic behavior of globally smooth solutions of the multidimensional isentropic hydrodynamic model for semiconductors abstract in this paper we study the asymptotic behavior of globally smooth solutions of the cauchy problem for the multidimensional isentropic hydrodynamic model for semiconductors in r d we prove that smooth solutions close to equilibrium of the problem converge to a stationary solution exponentially fast as t

bayesian image restoration an application to edge preserving surface recovery bayesian methods for recovering a 2 d surface are discussed it is assumed that there is a textural image that can be modeled by a markov random field and that the original surface is composed of different surfaces each of which is associated with one textural state both parametric and nonparametric methods are used to enforce smoothness of these surfaces iterative procedures are examined for simultaneous restoration of the textural image and estimation of underlying parameters from the estimated textural image and the estimated parameters an estimate for the original surface is obtained two illustrative examples are presented

boundary reconstruction in binary images using splines in image analysis it is often required to reconstruct the boundary of an object in a noisy image this paper presents a new method which relies on flexibility and computational simplicity of b spline curves to reconstruct a smooth connected boundary in a noisy binary image boundary inference is based on oriented distance functions yielding the estimator which is interpreted as a posterior expected boundary of the underlying random set the performance of the method and its dependence on the image quality and model specification are studied on simulated data the method is applied to reconstruct the skin air boundary in digitised analogue mammogram images highlightswe present a new method for boundary reconstruction in noisy images using b spline curves the method is bayesian and uses oriented distance functions for inference the resulting estimator can be interpreted as a posterior expected boundary we study the performance of the method on simulated data we apply the method to reconstruct the skin air boundary in mammogram images

singular perturbations of first order hyperbolic systems with stiff source terms abstract this work develops a singular perturbation theory for initial value problems of nonlinear first order hyperbolic systems with stiff source terms in several space variables it is observed that under reasonable assumptions many equations of classical physics of that type admit a structural stability condition this condition is equivalent to the well known subcharacteristic condition for one dimensional 2 2 systems and the well known time like condition for one dimensional scalar second order hyperbolic equations with a small positive parameter multiplying the highest derivatives under this stability condition we construct formal asymptotic approximations of the initial layer solution to the nonlinear problem furthermore assuming some regularity of the solutions to the limiting inner problem and the reduced problem we prove the existence of classical solutions in the uniform time interval where the reduced problem has a smooth solution and justify the validity of the formal approximations in any fixed compact subset of the uniform time interval the stability condition seems to be a key to problems of this kind and can be easily verified moreover this presentation unifies and improves earlier works for some specific equations

rigidity of invariant convex sets in symmetric spaces the main result implies that a proper convex subset of an irreducible higher rank symmetric space cannot have zariski dense stabilizer

convexity at infinity in cartan hadamard manifolds and applications to the asymptotic dirichlet and plateau problems we study the asymptotic dirichlet and plateau problems on cartan hadamard manifolds satisfying the so called strict convexity abbr sc condition the main part of the paper consists in studying the sc condition on a manifold whose sectional curvatures are bounded from above and below by certain functions depending on the distance to a fixed point in particular we are able to verify the sc condition on manifolds whose curvature lower bound can go to infty and upper bound to 0 simultaneously at certain rates or on some manifolds whose sectional curvatures go to infty faster than any prescribed rate these improve previous results of anderson borbely and ripoll and telichevsky we then solve the asymptotic plateau problem for locally rectifiable currents with mathbb z 2 multiplicity in acartan hadamard manifold satisfying the sc condition given any compact topologically embedded k 1 dimensional submanifold of partial infty m 2 le k le n 1 as the boundary data we also solve the asymptotic plateau problem for locally rectifiable currents with mathbb z multiplicity on any rotationally symmetric manifold satisfying the sc condition given a smoothly embedded submanifold as the boundary data these generalize previous results of anderson bangert and lang moreover we obtain new results on the asymptotic dirichlet problem for a large class of pdes in particular we are able to prove the solvability of this problem on manifolds with super exponential decay to infty of the curvature

on the bounded cohomology of semi simple groups s arithmetic groups and products we prove vanishing results for lie groups and algebraic groups over any local field in bounded cohomology the main result is a vanishing below twice the rank for semi simple groups related rigidity results are established for s arithmetic groups and groups over global fields we also establish vanishing and cohomological rigidity results for products of general locally compact groups and their lattices

divergence and quasimorphisms of right angled artin groups we give a group theoretic characterization of geodesics with superlinear divergence in the cayley graph of a right angled artin group a with connected defining graph we use this to prove that the divergence of a is linear if is a join and quadratic otherwise as an application we give a complete description of the cut points in any asymptotic cone of a we also show that every non abelian subgroup of a has an infinite dimensional space of non trivial quasimorphisms

dirichlet conditions at infinity for parabolic and elliptic equations we investigate existence and uniqueness of bounded solutions of parabolic equations with unbounded coefficients in rn r under specific assumptions we establish existence of solutions satisfying prescribed conditions at infinity depending on the direction along which infinity is approached moreover the large time behavior of such solutions is addressed we consider also elliptic equations in rn with similar conditions at infinity

c c simplicity and the amenable radical a countable group is c simple if its reduced c algebra is simple it is well known that c simplicity implies that the amenable radical of the group must be trivial we show that the converse does not hold by constructing explicit counter examples we additionally prove that every countable group embeds into a countable group with trivial amenable radical and that is not c simple

some unique group measure space decomposition results using an approach emerging from the theory of closable deriva tions on von neumann algebras we exhibit a class of groups cr satisfying the following property given any groups 1 2 2 cr then any free ergodic measure preserving action on a probability space 1 2 y x gives rise to a von neumann algebra with unique group measure space cartan subalgebra pairing this result with popa s orbit equivalence superrigidity theorem we obtain new examples of w superrigid actions

classical solutions and the glassey strauss theorem for the 3d vlasov maxwell system r glassey and w strauss have proved in arch rational mech anal 92 1986 59 90 that c1 solutions to the relativistic vlasov maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded the present paper simplifies their proof

poisson boundary of a relativistic diffusion in this article we study the asymptotic behaviour of a random motion in minkowski spacetime representing the random evolution of an object or signal traveling at a speed strictly less than the speed of the light introduced by dudley in his article ark mat 6 241 268 1966 we determine its invariant algebra and give an explicit description of the poisson boundary of its differential generator

property t and rigidity for actions on banach spaces we study property t and the fixed point property for actions on lp and other banach spaces we show that property t holds when l2 is replaced by lp and even a subspace quotient of lp and that in fact it is independent of 1 p we show that the fixed point property for lp follows from property t when 1 p 2 e for simple lie groups and their lattices we prove that the fixed point property for lp holds for any 1 p if and only if the rank is at least two finally we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive banach spaces

orbit equivalence rigidity and bounded cohomology we establish new results and introduce new methods in the theory of measurable orbit equivalence using bounded cohomology of group representations our rigidity statements hold for a wide uncountable class of groups arising from negative curvature geometry amongst our applications are a measurable mostow type rigidity theorems for products of negatively curved groups b prime factorization results for measure equivalence c superrigidity for orbit equivalence d the first examples of continua of type ii1 equivalence relations with trivial outer automorphism group that are mutually not stably isomorphic

coping with discontinuities in computer vision their detection classification and measurement the general principles of detection classification and measurement of discontinuities are studied the following issues are discussed detecting the location of discontinuities classifying discontinuities by their degrees measuring the size of discontinuities and coping with the random noise and designing optimal discontinuity detectors an algorithm is proposed for discontinuity detection from an input signal s for degree k discontinuity detection and measurement a detector p phi is used where p is the pattern and phi is the corresponding filter if there is a degree k discontinuity at location t sub 0 then in the filter response there is a scaled pattern alpha p at t sub 0 where alpha is the size of the discontinuity this reduces the problem to searching for the scaled pattern in the filter response a statistical method is proposed for the approximate pattern matching to cope with the random noise a study is made of optimal detectors which minimize the effects of noise

martin compactification of a complete surface with negative curvature in this paper we consider the martin compactification associated with the operator mathcal l delta 1 of a complete non compact surface sigma 2 with negative curvature in particular we investigate positive eigenfunctions with eigenvalue one of the laplace operator delta of sigma 2 and prove a uniqueness result such eigenfunctions are unique up to a positive multiplicative constant if they vanish on the part of the geometric boundary s infty sigma 2 of sigma 2 where the curvature is bounded above by a negative constant and satisfy some growth estimate on the other part of s infty sigma 2 where the curvature approaches zero this uniqueness result plays an essential role in our recent paper cao and he infinitesimal rigidity of steady gradient ricci soliton in dimension three arxiv 1412 2714 2014 preprint in which we prove an infinitesimal rigidity theorem for deformations of certain three dimensional collapsed gradient steady ricci soliton with a non trivial killing vector field

negatively curved manifolds elliptic operators and the martin boundary consider a riemannian manifold m of dimension n 2 and assume that m is complete simply connected and that its sectional curvatures are bounded between two negative constants in a recent paper 7 m anderson and r schoen have proved that the martin boundary of m with respect to the laplace beltrami operator a is naturally homeomorphic to soo m the sphere at infinity of m here we shall first establish a similar result for a wide class of elliptic operators on m giving at the same time a new proof of the theorem of anderson and schoen our proof relies heavily on several concepts of potential theory but on the other hand avoids the quite difficult calculations of 7 and perhaps makes the result more understandable roughly speaking we show that if y is a second order elliptic operator defined over m and has a uniformly nice behaviour on each ball of radius 1 in m then dq m the y martin boundary of m is s m provided that the following condition holds there is a positive y ci superharmonic function on m for some positive if instead we only assume the existence of the green function for y a minimal requirement when studying the y martin boundary then d m may be very different from so m even for a rotation invariant operator y on the unit ball of rn equipped

on the structural theory of ii1 factors of negatively curved groups ii actions by product groups abstract this paper contains a series of structural results for von neumann algebras arising from measure preserving actions by product groups on probability spaces expanding upon the methods used earlier by the first two authors we obtain new examples of strongly solid factors as well as von neumann algebras with unique or no cartan subalgebra for instance we show that every ii 1 factor associated with a weakly amenable group in the class s of ozawa is strongly solid there is also the following product version of this result any maximal abelian subalgebra of any ii 1 factor associated with a finite product of weakly amenable groups in the class s of ozawa has an amenable normalizing algebra finally pairing some of these results with a cocycle superrigidity result of ioana it follows that compact actions by finite products of lattices in s p n 1 n 2 are virtually w superrigid

cohomology of buildings and of their automorphism groups buildings were created by tits they serve as a vehicle for understanding real semi simple groups and their p adic analogs these are undoubtedly the two most interesting cases but existing constructions provide many more interesting examples some of which are remarkably symmetric while classical spherical or euclidean buildings correspond to spherical or euclidean reflection groups we are mainly concerned with buildings related to other infinite reflection groups the class of examples which this paper addresses is that of kac moody buildings as described by tits ti it is a very large family and it is precisely the great symmetry of these buildings that we are using our initial interest in the cohomology of buildings was that we suspected that buildings provided a rich source of kazhdan groups recall that a locally compact group g is a kazhdan group or has property t if the trivial representation of g is isolated in the space of all irreducible unitary representations of g equivalently g is a kazhdan group if h1 ct g 0 i e its first continuous cohomology group with coefficients in any unitary representation vanishes in this paper we use the latter definition for their equivalence cf hv it turns out that not only can we give an almost definitive statement about when the automorphism group of a kac moody

bayesian object identification this paper addresses the task of locating and identifying an unknown number of objects of different types in an image baddeley van lieshout 1993 advocate marked point processes as object priors whereas grenander miller 1994 use deformable template models in this paper elements of both approaches are combined to handle scenes containing variable numbers of objects of different types using reversible jump markov chain monte carlo methods for inference green 1995 the naive application of these methods here leads to slow mixing and we adapt the model and algorithm in tandem in proposing three strategies to deal with this the first two expand the model space by introducing an additional unknown object type and the idea of a variable resolution template the third strategy utilising the first two augments the algorithm with classes of updates which provide intuitive transitions between realisations containing different numbers of cells by splitting or merging nearby objects

stability of periodic steady state solutions to a non isentropic euler poisson system abstract we study the stability of periodic smooth solutions near non constant steady states for a non isentropic euler poisson system without temperature damping term the system arises in the theory of semiconductors for which the doping profile is a given smooth function in this stability problem there are no special restrictions on the size of the doping profile but only on the size of the perturbation we prove that small perturbations of periodic steady states are exponentially stable for large time for this purpose we introduce new variables and choose a non diagonal symmetrizer of the full euler equations to recover dissipation estimates this also allows to make the proof of the stability result very simple and concise

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

stability of steady states of the compressible euler poisson system in r 3 abstract we investigate the global existence and asymptotic behavior of smooth solutions near a non flat steady state to the compressible euler poisson system in r 3 using some concise energy estimates and an interpolation trick we refine the global existence and show that the solution converges to the stationary solution exponentially fast we assume that the h 3 norms of the initial density and velocity are small but the higher derivatives can be arbitrarily large in this sense our method simplifies the proof of hsiao et al 2003 17 and improves the results of it

product groups acting on manifolds we analyse volume preserving actions of product groups on riemannian manifolds under a natural spectral irreducibility assumption we prove the following dichotomy either the action is measurably isometric in which case there are at most two factors or the action is infinitesimally linear which means that the derivative cocycle arises from unbounded linear representations of all factors as a first application this provides lower bounds on the dimension of the manifold in terms of the number of factors in the acting group another application is a strong restriction for actions of non linear groups we prove our results by means of a new cocycle superrigidity theorem of independent interest in analogy to zimmer s programme

fixed points and amenability in non positive curvature consider a proper cocompact cat 0 space x we give a complete algebraic characterisation of amenable groups of isometries of x for amenable discrete subgroups an even narrower description is derived implying mathbf q linearity in the torsion free case we establish levi decompositions for stabilisers of points at infinity of x generalising the case of linear algebraic groups to text is x a geometric counterpart of this sheds light on the refined bordification of x a la karpelevich and leads to a converse to the adams ballmann theorem it is further deduced that unimodular cocompact groups cannot fix any point at infinity except in the euclidean factor this fact is needed for the study of cat 0 lattices various fixed point results are derived as illustrations

unbounded positive entire solutions of rotationally symmetric harmonic map equations abstract we study the existence of unbounded positive entire c 2 solutions of the rotationally symmetric harmonic map equations using the existence result we solve the dirichlet problem at infinity for any nonnegative boundary value at infinity

boundary detection through dynamic polygons a method for the bayesian restoration of noisy binary images portraying an object with constant grey level on a background is presented the restoration performed by fitting a polygon with any number of sides to the object s outline is driven by a new probabilistic model for the generation of polygons in a compact subset of r 2 which is used as a prior distribution for the polygon some measurability issues raised by the correct specification of the model are addressed the simulation from the prior and the calculation of the a posteriori mean of grey levels are carried out through reversible jump markov chain monte carlo computation whose implementation and convergence properties are also discussed one example of restoration of a synthetic image is presented and compared with existing pixel based methods

asymptotic behavior of the solution to a nonisentropic hydrodynamic model of semiconductors abstract we study the asymptotic behavior of the solution for a hydrodynamic model of semiconductors where the energy equation is included we study the case where the flow is subsonic and the doping profile is close to a negative constant depending on the spacial variablex we shall show that a given steady state solution is asymptotically stable or unstable depending on whether or not the density of the initial data satisfiesp 0 wherepis defined in 3 5

large time behavior of the solutions to a hydrodynamic model for semiconductors we establish the global existence of smooth solutions to the cauchy problem for the one dimensional isentropic euler poisson or hydrodynamic model for semiconductors for small initial data in particular we show that as t to infty these solutions converge to the stationary solutions of the drift diffusion equations the existence and uniqueness of stationary solutions to the drift diffusion equations are proved without the smallness assumption

superrigidity for irreducible lattices and geometric splitting we prove general superrigidity results for actions of irreducible lattices on cat 0 spaces first in terms of the ideal boundary and then for the intrinsic geometry including for infinite dimensional spaces in particular one obtains a new and self contained proof of margulis superrigidity theorem for uniform irreducible lattices in non simple groups the proofs rely on simple geometric arguments including a splitting theorem which can be viewed as an infinite dimensional and singular generalization of the lawson yau gromoll wolf theorem appendix a gives a very elementary proof of commensurator superrigidity appendix b proves that all our results also hold for certain non uniform lattices

integrable measure equivalence and rigidity of hyperbolic lattices we study rigidity properties of lattices in operatorname isom mathbf h n simeq mathrm so n 1 mathbb r n 3 and of surface groups in operatorname isom mathbf h 2 simeq mathrm sl 2 mathbb r in the context of integrable measure equivalence the results for lattices in operatorname isom mathbf h n n 3 are generalizations of mostow rigidity they include a cocycle version of strong rigidity and an integrable measure equivalence classification despite the lack of mostow rigidity for n 2 we show that cocompact lattices in operatorname isom mathbf h 2 allow a similar integrable measure equivalence classification

integrability of induction cocycles for kac moody groups we prove that whenever a kac moody group over a finite field is a lattice of its buildings it has a fundamental domain with respect to which the induction cocycle is lp for any p 1 the proof uses elementary counting arguments for root group actions on buildings the applications are the possibility to apply some lattice superrigidity and the normal subgroup property for kac moody lattices

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

an image analysis problem in electron microscopy abstract this article considers the problem of identifying the irregular boundary of a magnetic domain in a thin multilayer film using data in the form of an electron micrograph two approaches are illustrated both of which are based on the concept of two smooth intensity surfaces one corresponding to the domain and one corresponding to the background so that the objective is to determine the boundary between the parts of the image where the two surfaces are present in the first a hierarchical bayesian approach priors are assumed for the set of domain background states and for the two intensity surfaces and restoration is carried out using a version of besag s icm procedure it is shown that it is important to initialize the method efficiently the second approach uses a template like model for the boundary and also relies on a bayesian approach the results from the second approach can be used as an end in themselves or as a way of initializing the more flexible first approach several illustrati

superrigidity of actions on finite rank median spaces abstract finite rank median spaces are a simultaneous generalisation of finite dimensional cat 0 cube complexes and real trees if is an irreducible lattice in a product of rank one simple lie groups we show that every action of on a complete finite rank median space has a global fixed point this is in sharp contrast with the behaviour of actions on infinite rank median spaces where even proper cocompact actions can arise the fixed point property is obtained as corollary to a superrigidity result the latter holds for irreducible lattices in arbitrary products of compactly generated topological groups we exploit roller compactifications of median spaces these were introduced in 48 and generalise a well known construction in the case of cube complexes we show that the haagerup cocycle provides a reduced 1 cohomology class that detects group actions with a finite orbit in the roller compactification this is new even for cat 0 cube complexes and has interesting consequences involving shalom s property h f d for instance in gromov s density model random groups at low density do not have h f d

geometry of the mapping class groups i boundary amenability we construct a geometric model for the mapping class group mathcal m mathcal c mathcal g of a non exceptional oriented surface s of genus g with k punctures and use it to show that the action of mathcal m mathcal c mathcal g on the compact metrizable hausdorff space of complete geodesic laminations for s is topologically amenable as a consequence the novikov higher signature conjecture holds for every subgroup of mathcal m mathcal c mathcal g

on splitting theorems for cat 0 spaces and compact geodesic spaces of non positive curvature in this paper we show some splitting theorems for cat 0 spaces on which a product group acts geometrically and we obtain a splitting theorem for compact geodesic spaces of non positive curvature a cat 0 group is said to be rigid if determines its boundary up to homeomorphisms of a cat 0 space on which acts geometrically c croke and b kleiner have constructed a non rigid cat 0 group as an application of the splitting theorems for cat 0 spaces we obtain that if 1 and 2 are rigid cat 0 groups then so is 1 2

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

at infinity of finite dimensional cat 0 spaces we show that any filtering family of closed convex subsets of a finite dimensional cat 0 space x has a non empty intersection in the visual bordification x over bar x boolean or partial derivative x using this fact several results known for proper cat 0 spaces may be extended to finite dimensional spaces including the existence of canonical fixed points at infinity for parabolic isometries algebraic and geometric restrictions on amenable group actions and geometric superrigidity for non elementary actions of irreducible uniform lattices in products of locally compact groups

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

harmonic maps between 3 dimensional hyperbolic spaces we prove that a quasiconformal map of the sphere s 2 admits a harmonic quasi isometric extension to the hyperbolic space h 3 thus confirming the well known schoen conjecture in dimension 3

on the density of geometrically finite kleinian groups the density conjecture of bers sullivan and thurston predicts that each complete hyperbolic 3 manifold m with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3 manifolds we prove that the conjecture obtains for each complete hyperbolic 3manifold with no cusps and incompressible ends

cat 1 spaces divergence groups and their commensurators a cat 1 space is a metric geodesic space in which every geodesic triangle is thinner than its associated comparison triangle in the hyperbolic plane b briha gr the cat 1 property is one among many possible generalizations to singular spaces of the notion of negative curvature important examples of cat 1 spaces include riemannian manifolds of sectional curvature k 1 and their convex subsets b g s metric trees and piecewise hyperbolic cell complexes mou da hag be 1 be 2 b br in this paper we establish certain superrigidity results for isometric actions of a group on a cat 1 space in the following two settings a the group is a subgroup of a locally compact group g with comg where g is a sufficiently large discrete subgroup and comg g g g 1 g and share a subgroup of finite index is the commensurator of in g b the group is an irreducible lattice in g n 1g k where each g is a semisimple algebraic group defined over a local field k the issues addressed in this paper are motivated on one hand by earlier work of g a margulis ma dealing with the linear representation theory of where in case a g is a semisimple group and g a lattice and on the other hand by the results of lubotzky mozes and zimmer l m z concerning isometric actions of on trees where comg g is the group of automorphisms of a regular tree and g is a lattice our approach to establishing superrigidity results is based on ergodic theoretic methods developed by margulis ma zi 3 a c b in this context the following notion of boundary of a locally compact group will be useful let b be a standard borel space on which acts by borel automorphisms preserving a finite measure class

cocycle superrigidity and bounded cohomology for negatively curved spaces we introduce new techniques to extend superrigidity theory beyond the scope of lie or algebraic groups we construct a cohomological invariant which accounts for and generalizes all known superrigidity results for actions on negatively curved spaces together with a new vanishing result and the machinery of bounded cohomology this enables us to prove a general superrigidity theorem for actions of irreducible lattices on spaces of negative curvature we also prove a cocycle version a la zimmer

rigidity for von neumann algebras given by locally compact groups and their crossed products we prove the first rigidity and classification theorems for crossed product von neumann algebras given by actions of non discrete locally compact groups we prove that for arbitrary free probability measure preserving actions of connected simple lie groups of real rank one the crossed product has a unique cartan subalgebra up to unitary conjugacy we then deduce a w strong rigidity theorem for irreducible actions of products of such groups more generally our results hold for products of locally compact groups that are nonamenable weakly amenable and that belong to ozawa s class mathcal s

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

euler and navier stokes equations on the hyperbolic plane we show that nonuniqueness of the leray hopf solutions of the navier stokes equation on the hyperbolic plane 2 observed by chan and czubak is a consequence of the hodge decomposition we show that this phenomenon does not occur on n whenever n 3 we also describe the corresponding general hamiltonian framework of hydrodynamics on complete riemannian manifolds which includes the hyperbolic setting

an exotic deformation of the hyperbolic space let isom h n be the group of isometries of the n dimensional real hyperbolic space we first classify all continuous non elementary actions of on the infinite dimensional real hyperbolic space we then prove the existence of a continuous family of non isometric minimal proper cat 1 spaces on which isom h n acts cocompactly by isometries

boundary behavior of harmonic maps on non smooth domains and complete negatively curved manifolds abstract in this paper we develop a theory for harmonic maps which is analogous to the classical theory for bounded harmonic functions in harmonic analysis we solve the dirichlet problem in bounded lipschitz domains and manifolds with negative sectional curvatures generalize the wienner criterion and prove the fatou theorem for harmonic maps into convex balls

the oshima sekiguchi and liouville theorems on heintze groups abstract let l be an elliptic operator on a riemannian manifold m a function f annihilated by l is said to be l harmonic f is said to have moderate growth if and only if f grows at most exponentially in the riemannian distance if m is a rank one symmetric space and l is the laplace beltrami operator for m the oshima sekiguchi theorem t oshima j sekiguchi eigenspaces of invariant differential operators on an affine symmetric space invent math 57 1980 1 81 states that a l harmonic function f has moderate growth if and only if f is the poisson integral of a distribution on the furstenberg boundary in this work we prove that this result generalizes to a very large class of homogeneous riemannian manifolds of negative curvature we also i prove a liouville type theorem that characterizes the polynomial like harmonic functions which vanish on the boundary in terms of their growth properties ii describe all polynomial like harmonic functions and iii give asymptotic expansions for the poisson kernel one consequence of this work is that every schwartz distribution on the boundary is the boundary value for a l harmonic function f which is uniquely determined modulo polynomial like harmonic functions

on the superrigidity of malleable actions with spectral gap some of the most interesting aspects of the dynamics of measure preserving actions of countable groups on probability spaces v rx x are revealed by the study of group measure space von neumann algebras l x x t mvnl and the classification of actions up to orbit equivalence oe i e up to isomorphism of probability spaces carrying the orbits of actions onto each other although one is in von neumann algebras and the other in ergodic theory the two problems are closely related as an oe of actions v rx x a rxy has been shown to implement an algebra isomorphism l x x t l y x a taking l x onto l y and vice versa si dy fm in particular the isomorphism class of l x xi t only depends on the equivalence relation 7 r t gt 1t x g t thus von neumann equivalence vne of group actions requiring isomorphism of their group measure space algebras is weaker than oe since there are exam ples of non oe actions whose associated von neumann algebras are all isomorphic cj1 it is in general strictly weaker on the other hand oe is manifestly weaker than classical conjugacy which for free actions r rx x a rx y requires isomor phism of probability spaces a x p y v satisfying ar a 1 a so in particular r a how much weaker vne and oe can be with respect to conju gacy is best seen in the amenable case where by a celebrated theorem of connes all free ergodic actions of all infinite amenable groups give rise to the same hi factor cl and by dy ow cfw they are undistinguishable under oe as well also any embedding of algebras l x xi t c l y x a with a amenable forces t to be amenable but the non amenable case is extremely complex and for many years progress has been slow mvn2 dy me c2 cw sc even after the discovery of the first rigidity phenomena by connes in von neumann algebras c3 c4 and by zimmer in oe ergodic theory zi z2 this changed dramatically over the last 7 8 years with the advent of a variety of striking rigidity results ful gl g2 mosh h hk p1 p8 see p9 for a survey also sh for a survey on oe rigidity our aim in this paper is to investigate the most extreme such phenomena called strong rigidity which show that for certain classes of source group actions

some uniqueness and nonexistence theorems for embedded minimal surfaces thanks to the works of callahan costa hoffman karcher meeks rosenberg wei etc see for example 1 2 3 5 8 11 12 16 20 we dispose now of a large number of properly embedded minimal surfaces in the euclidean space ir other than the classical examples all those surfaces can be viewed as minimal surfaces with finite total curvature properly embedded in complete flat three manifolds the most basic invariants associated to a surface of this type are its topology and its periodicity it is an interesting problem to decide if the simplest examples like the catenoid the helicoid the scherk s surfaces or the riemann example can be characterized in terms of some of these invariants in the non periodic case there are two important uniqueness theorems in this direction the first one obtained by schoen 17 characterizes the catenoid as the only complete minimal surface embedded

cocycle superrigidity for translation actions of product groups let g be either a profinite or a connected compact group and be finitely generated dense subgroups assuming that the left translation action of on g is strongly ergodic we prove that any cocycle for the left right translation action of on g with values in a countable group is virtually cohomologous to a group homomorphism moreover we prove that the same holds if g is a not necessarily compact connected simple lie group provided that contains an infinite cyclic subgroup with compact closure we derive several applications to oe and w superrigidity in particular we obtain the first examples of compact actions of f2 f2 which are w superrigid

brownian motion and dirichlet problems at infinity we discuss angular convergence of riemannian brownian motion on a cartan hadamard manifold and show that the dirichlet problem at infinity for such a manifold is uniquely solvable under the curvature conditions ce 2 ar x km x a2 vspace 0 5pt 0 and cr x 2 km x 1 r x 2 2 2 respectively

compact object recognition using energy function based optimization describes a method of recognizing objects whose contours can be represented in smoothly varying polar coordinate form both low and high level information about the object contour smoothness and edge sharpness at the low level and contour shape at the high level are incorporated into a single energy function that defines a 1d cyclic markov random field 1dcmrf this 1dcmrf is based on a polar coordinate object representation whose center can be initialized at any location within the object the recognition process is based on energy function minimization which is implemented by simulated annealing

the dirichlet problem at infinity for manifolds of negative curvature on considere l existence de fonctions harmoniques bornees sur des varietes simplement connexes n n de courbure negative