adaptive poromechanics computations based on a posteriori error estimates for fully mixed formulations of biot s consolidation model abstract this paper is concerned with the analysis of coupled mixed finite element methods applied to the biot s consolidation model we consider two mixed formulations that use the stress tensor and darcy velocity as primary variables as well as the displacement and pressure the first formulation is with a symmetric stress tensor while the other enforces the symmetry of the stress weakly through the introduction of a lagrange multiplier the well posedness of the two formulations is shown through galerkin s method and suitable a priori estimates the two formulations are then discretized with the backward euler scheme in time and with two mixed finite elements in space we present next a general and unified a posteriori error analysis which is applicable for any flux and stress conforming discretization our estimates are based on h 1 conforming reconstruction of the pressure and a suitable h 1 d conforming reconstruction of the displacement both are continuous and piecewise affine in time these reconstructions are used to infer a guaranteed and fully computable upper bound on the energy type error measuring the differences between the exact and the approximate pressure and displacement the error components resulting from the spatial and the temporal discretization are distinguished they are then used to design an adaptive space time algorithm numerical experiments illustrate the efficiency of our estimates and the performance of the adaptive algorithm

the goldie theorem for h semiprime algebras abstract the main result states that under certain assumptions about a hopf algebra h every h semiprime right noetherian h module algebra has a quasi frobenius classical right quotient ring another question treated in the paper is concerned with the extension of h module structures to quotient rings these results have an application to the semiprimeness problem for smash product algebras a h

complex earthquakes and teichmuller theory it is known that any two points in teichmuller space are joined by an earthquake path in this paper we show any earthquake path r t s extends to a proper holomorphic mapping of a simplyconnected domain d into teichmuller space where r d c these complex earthquakes relate weil petersson geometry projective structures pleated surfaces and quasifuchsian groups using complex earthquakes we prove grafting is a homeomorphism for all 1 dimensional teichmuller spaces and we construct bending coordinates on bers slices and their generalizations in the appendix we use projective surfaces to show the closure of quasifuchsian space is not a topological manifold

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

global well posedness theory for a class of coupled parabolic elliptic systems abstract we consider a fully coupled system consisting of a parabolic equation with boundary and initial conditions and an abstract elliptic equation in a variational form with time as a parameter such systems appear in applications related to the modeling of coupled diffusion and elastic deformation processes in inhomogeneous porous media within a quasi static assumption we establish the global existence uniqueness and continuous dependence on initial and boundary data of a weak solution to the system the proof of this result involves the proposed pseudo decoupling method which reduces the coupled system to an initial boundary value problem for a single implicit equation and a refined approach to deriving a priori energy estimates based on component wise contributions of system parameters to energy norms

diffusion in poro elastic media existence uniqueness and regularity theory is developed for a general initial boundary value problem for a system of partial differential equations which describes the biot consolidation model in poro elasticity as well as a coupled quasi static problem in thermoelasticity additional effects of secondary consolidation and pore fluid exposure on the boundary are included this quasi static system is resolved as an application of the theory of linear degenerate evolution equations in hilbert space and this leads to a precise description of the dynamics of the system

effective distance between nested margulis tubes we give sharp effective bounds on the distance between tori of fixed injectivityradius inside a margulis tube in a hyperbolic 3 manifold

hyperbolic cone manifolds short geodesics and schwarzian derivatives given a geometrically finite hyperbolic cone manifold with the cone singularity sufficiently short we construct a one parameter family of cone manifolds decreasing the cone angle to zero we also control the geometry of this one parameter family via the schwarzian derivative of the projective boundary and the length of closed geodesics

minimal co volume hyperbolic lattices ii simple torsion in a kleinian group this paper represents the nal step in solving the problem posed by siegel in 1945 of determining the minimal co volume lattices of hyperbolic 3 space h also problem 3 60 f in the kirby problem list from 1993 here we identify the two smallest co volume lattices both these groups are two generator arithmetic lattices generated by two elements of nite orders 2 and 3 their co volumes are 0 0390 and 0 0408 the precise values are given in terms of the dedekind zeta function of a number eld via a formula of borel our earlier work dealt with the cases when there is a nite spherical subgroup or high order torsion in the lattice thus here we are concerned with the study of simple torsion of low order and the geometric structure of klein 4 subgroups of a kleinian group we also identify certain universal geometric constraints imposed by discreteness on kleinian groups which are of independent interest to obtain these results we use a range of geometric and arithmetic criteria to obtain information on the structure of the singular set of the associated orbifold and then co volume bounds by studying equivariant neighbourhoods of xed point sets together with a rigorous computer search of certain parameter spaces for two generator kleinian groups

regenerating singular hyperbolic structures from sol let m be a torus bundle over s 1 with an orientation preserving anosov monodromy the manifold m admits a geometric structure modeled on sol we prove that the sol structure can be deformed into singular hyperbolic cone structures whose singular locus m is the mapping torus of the fixed point of the monodromy the hyperbolic cone metrics are parametred by the cone angle in the interval 0 2 when 2 the cone manifolds collapse to the basis of the fibration s 1 and they can be rescaled in the direction of the fibers to converge to the sol manifold

semisimple hopf actions on weyl algebras abstract we study actions of semisimple hopf algebras h on weyl algebras a over an algebraically closed field of characteristic zero we show that the action of h on a must factor through a group action in other words if h acts inner faithfully on a then h is cocommutative the techniques used include reduction modulo a prime number and the study of semisimple cosemisimple hopf actions on division algebras

cusp shapes under cone deformation a horospherical torus about a cusp of a hyperbolic manifold inherits a euclidean similarity structure called a cusp shape we bound the change in cusp shape when the hyperbolic structure of the manifold is deformed via cone deformation preserving the cusp the bounds are in terms of the change in structure in a neighborhood of the singular locus alone we then apply this result to provide information on the cusp shape of many hyperbolic knots given only a diagram of the knot specifically we show there is a universal constant c such that if a knot admits a prime twist reduced diagram with at least c crossings per twist region then the length of the second shortest curve on the cusp torus is bounded the bound is linear in the number of twist regions of the diagram

bounds on volume increase under dehn drilling operations in this paper we investigate how the volume of a hyperbolic manifold increases under the process of removing a curve that is dehn drilling if the curve we remove is a geodesic we show that for a certain family of manifolds the volume increase is bounded above by pi cdot l where l is the length of the geodesic drilled we further construct examples to show that there is no lower bound to the volume increase in terms of a monotonic unbounded function of length in particular this shows that volume increase is not bounded below linearly in length 1991 mathematics subject classification primary 51m10 51m20 secondary 51m25 52c25

laminations mesurees de plissage des varietes hyperboliques de dimension 3 for a hyperbolic metric on a 3 dimensional manifold the boundary of its convex core is a surface which is almost everywhere totally geodesic but which is bent along a family of disjoint geodesics the locus and intensity of this bending is described by a measured geodesic lamination which is a topological object we consider two problems the topological characterization of those measured geodesic laminations which can occur as bending measured laminations of hyperbolic metrics and the uniqueness problem which asks whether a hyperbolic metric is uniquely determined by its bending measured lamination

hyperbolic manifolds with convex boundary let m m be a 3 manifold which carries a hyperbolic metric with convex boundary we consider the hyperbolic metrics on m such that the boundary is smooth and strictly convex we show that the induced metrics on the boundary are exactly the metrics with curvature k 1 and that the third fundamental forms of m are exactly the metrics with curvature k 2 each is obtained exactly once

fixed points of compositions of earthquakes let s be a closed surface of genus at least 2 and consider two measured geodesic laminations that fill s right earthquakes along these laminations are diffeomorphisms of the teichmuller space of s we prove that the composition of these earthquakes has a fixed point in the teichmuller space another way to state this result is that it is possible to prescribe any two measured laminations that fill a surface as the upper and lower measured bending laminations of the convex core of a globally hyperbolic ads manifold the proof uses some estimates from the geometry of those ads manifolds

minimal co volume hyperbolic lattices i the spherical points of a kleinian group we identify the two minimal co volume lattices of the isometry group of hyperbolic 3 space that contain a finite spherical triangle group these two groups are arithmetic and are in fact the two minimal co volume lattices our results here represent the key step in establishing this fact thereby solving a problem posed by siegel in 1945 as a consequence we obtain sharp bounds on the order of the symmetry group of a hyperbolic 3 manifold in terms of its volume analogous to the hurwitz 84g 84 theorem of 1892 the finite spherical subgroups of a kleinian group give rise to the vertices of the singular graph in the quotient orbifold we identify the small values of the discrete spectrum of hyperbolic distances between these vertices and show these small values give rise to arithmetic lattices once vertices are sufficiently separated one obtains volume bounds by studying equivariant sets

dehn filling volume and the jones polynomial given a hyperbolic 3 manifold with torus boundary we bound the change in volume under a dehn filling where all slopes have length at least 2 this result is applied to give explicit diagrammatic bounds on the volumes of many knots and links as well as their dehn fillings and branched covers finally we use this result to bound the volumes of knots in terms of the coefficients of their jones polynomials

cones embedded in hyperbolic manifolds we show that the existence of a maximal embedded tube in a hyperbolic n manifold implies the existence of a certain conical region one application is to establish a lower bound on the volume of the region outside the tube thereby improving estimates on volume and estimates on lengths of geodesics in small volume hyperbolic 3 manifolds we also provide new bounds on the injectivity radius and diameter of an n manifold

lattices of minimum covolume in chevalley groups over local fields of positive characteristic in this article we show that if g is a simply connected chevalley group of either classical type of rank bigger than 1 or type e6 and q 9 is a power of a prime number p 5 then g g fq t 1 up to an automorphism has a unique lattice of minimum covolume which is g fq t 1

finite dehn surgery on knots let k be a knot with a closed tubular neighbourhood n k in a connected orientable closed 3 manifold w such that the exterior of k m w intn k is irreducible we consider the problem of which dehn surgeries on k or equivalently which dehn fillings on m can produce 3 manifolds with finite fundamental group for convenience a surgery is called a g surgery if the resultant 3 manifold has fundamental group g if g is cyclic or finite the surgery is also called a cyclic surgery or a finite surgery similar terminology will be used for dehn fillings the manifold obtained by the dehn filling on m along m with slope r is denoted by m r let r1 r2 denote the minimal geometric intersection number the distance between two slopes r1 and r2 on m according to t1 m belongs to one of the following three mutually exclusive categories i m is a seifert fibred space admitting no essential torus ii m is a hyperbolic manifold i e intm admits a complete hyperbolic metric of finite volume iii m contains an essential torus it is a remarkable result the so called cyclic surgery theorem cgls that if m is not seifert fibred then all cyclic surgery slopes of k have mutual distance no larger than 1 and consequently there are at most 3 cyclic surgeries on k in this paper we consider finite dehn surgery on k and we prove for instance that if m is not a manifold of type i and is not a union along a torus of the twisted i bundle over the klein bottle and a cabled space then there are at most 6 finite and cyclic surgeries on k of maximal mutual distance 5 henceforth we shall use finite cyclic to mean either finite or infinite cyclic it turns out to be convenient to consider the three cases mentioned above separately in case i it is well known that one can completely classify the finite cyclic surgeries on k considering the torus knots for instance one sees that there exist infinitely many knots whose exteriors are of type i each of which admit an infinity of distinct finite cyclic or non cyclic surgery slopes our contributions deal with the cases ii and iii for the former we obtain

a robust linearization scheme for finite volume based discretizations for simulation of two phase flow in porous media in this work we consider a mathematical model for two phase flow in porous media the fluids are assumed immiscible and incompressible and the solid matrix non deformable the mathematical model for the two phase flow is written in terms of the global pressure and a complementary pressure obtained by using the kirchhoff transformation as primary unknowns for the spatial discretization finite volumes have been used more precisely the multi point flux approximation method and in time the backward euler method has been employed we present here a new linearization scheme for the nonlinear system arising after the temporal and spatial discretization we show that the scheme is linearly convergent numerical experiments are presented that sustain the theoretical results

lower bounds on volumes of hyperbolic haken 3 manifolds we prove a volume inequality for 3 manifolds having c o metrics bent along a surface and satisfying certain curvature conditions the result makes use of perelman s work on the ricci flow and geometrization of closed 3 manifolds corollaries include a new proof of a conjecture of bonahon about volumes of convex cores of kleinian groups improved volume estimates for certain haken hyperbolic 3 manifolds and a lower bound on the minimal volume of orientable hyperbolic 3 manifolds an appendix compares estimates of volumes of hyperbolic 3 manifolds drilled along a closed embedded geodesic with experimental data

projective structures with degenerate holonomy and the bers density conjecture we prove the bers density conjecture for singly degenerate kleinian surface groups without parabolics

pinching constants for hyperbolic manifolds we show in this paper that for everyn 4 there exists a closedn dimensional manifoldv which carries a riemannian metric with negative sectional curvaturek but which admits no metric with constant curvaturek 1 we also estimate the pinching constantsh for which our manifoldsv admit metrics with 1 k h

a pi degree theorem for quantum deformations abstract we prove that if a filtered quantization a of a finitely generated commutative domain over a field k is a pi algebra then a is commutative if char k 0 and its pi degree is a power of p if char k p

axial distances in discrete mobius groups abstract we describe here new lower bounds for the trace of the commutator of a discrete two generator group of mobius transformations these results lead to sharp estimates for the distance between the axes of elliptics in a discrete group and hence to new bounds for the volume of hyperbolic manifolds and orbifolds that will be discussed elsewhere

monolithic and splitting solution schemes for fully coupled quasi static thermo poroelasticity with nonlinear convective transport abstract this paper concerns monolithic and splitting based iterative procedures for the coupled nonlinear thermo poroelasticity model problem the thermo poroelastic model problem we consider is formulated as a three field system of pde s consisting of an energy balance equation a mass balance equation and a momentum balance equation where the primary variables are temperature fluid pressure and elastic displacement due to the presence of a nonlinear convective transport term in the energy balance equation it is convenient to have access to both the pressure and temperature gradients hence we introduce these as two additional variables and extend the original three field model to a five field model for the numerical solution of this five field formulation we compare six approaches that differ by how we treat the coupling decoupling between the flow and from heat and from the mechanics suitable for varying coupling strength between the three physical processes the approaches have in common a simultaneous application of the so called l scheme which works both to stabilize iterative splitting as well as to linearize nonlinear problems and can be seen as a generalization of the undrained and fixed stress split algorithms more precisely the derived procedures transform a nonlinear and fully coupled problem into a set of simpler subproblems to be solved sequentially in an iterative fashion we provide a convergence proof for the derived algorithms and demonstrate their performance through several numerical examples investigating different strengths of the coupling between the different processes

space time finite element approximation of the biot poroelasticity system with iterative coupling abstract we analyze an optimized artificial fixed stress iterative scheme for a space time finite element approximation of the biot system modeling fluid flow in deformable porous media the iteration is based on a prescribed constant artificial volumetric mean total stress in the first half step the optimization comes through the adaptation of a numerical stabilization or tuning parameter and aims at an acceleration of the iterations the separated subproblems of fluid flow written as a mixed first order in space system and mechanical deformation are discretized by space time finite element methods of arbitrary order continuous and discontinuous galerkin discretizations of the time variable are encountered the convergence of the iterative schemes is proved for the continuous and fully discrete case the choice of the optimization parameter is identified in the proofs of convergence of the iterations the analyses are illustrated and confirmed by numerical experiments

the maximal number of exceptional dehn surgeries thurston s hyperbolic dehn surgery theorem is one of the most important results in 3 manifold theory and it has stimulated an enormous amount of research if m is a compact orientable hyperbolic 3 manifold with boundary a single torus then the theorem asserts that for all but finitely many slopes s on m the manifold m s obtained by dehn filling along s also admits a hyperbolic structure the slopes s where m s is not hyperbolic are known as exceptional a major open question has been what is the maximal number of exceptional slopes on such a manifold m when m is the exterior of the figure eight knot the number of exceptional slopes is 10 and this was conjectured by gordon in 19 to be an upper bound that holds for all m in this paper we prove this conjecture

finite dimensional hopf actions on weyl algebras abstract we prove that any action of a finite dimensional hopf algebra h on a weyl algebra a over an algebraically closed field of characteristic zero factors through a group action in other words weyl algebras do not admit genuine finite quantum symmetries this improves a previous result by the authors where the statement was established for semisimple h the proof relies on a refinement of the method previously used namely considering reductions of the action of h on a modulo prime powers rather than primes we also show that the result holds more generally for algebras of differential operators this gives an affirmative answer to a question posed by the last two authors

homotopy hyperbolic 3 manifolds are hyperbolic this paper introduces a rigorous computer assisted procedure for analyzing hyperbolic 3 manifolds this procedure is used to complete the proof of several long standing rigidity conjectures in 3 manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3 manifold

the grafting map of teichmuller space one of the underlying principles in the study of kleinian groups is that aspects of the complex projective geometry of quotients of by these groups reflect properties of the three dimensional hyperbolic geometry of the quotients ofh by these groups yet even though it has been over thirty five years since lipman bers exhibited a holomorphic embedding of the teichmuller space of riemann surfaces in terms of the projective geometry of a teichmuller space of quasi fuchsian manifolds no corresponding embedding in terms of the three dimensional hyperbolic geometry has been presented one of the goals of this paper is to give such an embedding this embedding is straightforward and has been expected for some time ta97 mc98 to each member of a bers slice of the space qf of quasi fuchsian 3manifolds we associate the bending measured lamination of the convex hull facing the fixed conformal end the geometric relationship between a boundary component of a convex hull and the projective surface at infinity for its end is given by a process known as grafting an operation on projective structures on surfaces that traces its roots back at least to klein kl33 p 230 50 with a modern history developed by many authors ma69 he75 fa83 st83 go87 gkm00 ta97 mc98 the main technical tool in our proof that bending measures give coordinates for bers slices and the second major goal of this paper is the completion of the proof of the grafting conjecture this conjecture states that for a fixed measured lamination the self map of teichmuller space induced by grafting a surface along is a homeomorphism of teichmuller space our contribution to this argument is a proof of the injectivity of the grafting map while the principal application of this result that we give is to geometric coordinates on the bers slice of qf one expects that the grafting homeomorphism might lead to other systems of geometric coordinates for other families of kleinian groups see 5 2 thus we feel that this result is of interest in its own right we now state our results and methods more precisely throughout s will denote a fixed differentiable surface which is closed orientable and of genus g 2 let tg be the corresponding teichmuller space of marked conformal structures on s and let pg denote the deformation space of complex projective structures on s see 2 for definitions

recognizing a relatively hyperbolic group by its dehn fillings dehn fillings for relatively hyperbolic groups generalize the topological dehn surgery on a non compact hyperbolic 3 manifold such as a hyperbolic knot complement we prove a rigidity result saying that if two non elementary relatively hyperbolic groups without suitable splittings have sufficiently many isomorphic dehn fillings then these groups are in fact isomorphic our main application is a solution to the isomorphism problem in the class of non elementary relatively hyperbolic groups with residually finite parabolic groups and with no suitable splittings

parameter robust discretization and preconditioning of biot s consolidation model biot s consolidation model in poroelasticity has a number of applications in science medicine and engineering the model depends on various parameters and in practical applications these parameters range over several orders of magnitude a current challenge is to design discretization techniques and solution algorithms that are well behaved with respect to these variations the purpose of this paper is to study finite element discretizations of this model and construct block diagonal preconditioners for the discrete biot systems the approach taken here is to consider the stability of the problem in nonstandard or weighted hilbert spaces and employ the operator preconditioning approach we derive preconditioners that are robust with respect to both the variations of the parameters and the mesh refinement the parameters of interest are small time step sizes large bulk and shear moduli and small hydraulic conductivity

well posedness of the fully coupled quasi static thermo poroelastic equations with nonlinear convective transport abstract this paper is concerned with the analysis of the quasi static thermo poroelastic model this model is nonlinear and includes thermal effects compared to the classical quasi static poroelastic model also known as biot s model it consists of a momentum balance equation a mass balance equation and an energy balance equation fully coupled and nonlinear due to a convective transport term in the energy balance equation the aim of this article is to investigate in the context of mixed formulations the existence and uniqueness of a weak solution to this model problem the primary variables in these formulations are the fluid pressure temperature and elastic displacement as well as the darcy flux heat flux and total stress the well posedness of a linearized formulation is addressed first through the use of a galerkin method and suitable a priori estimates this is used next to study the well posedness of an iterative solution procedure for the full nonlinear problem a convergence proof for this algorithm is then inferred by a contraction of successive difference functions of the iterates using suitable norms

universal bounds for hyperbolic dehn surgery this paper gives a quantitative version of thurston s hyperbolic dehn surgery theorem applications include the first universal bounds on the number of nonhyperbolic dehn fillings on a cusped hyperbolic 3 manifold and estimates on the changes in volume and core geodesic length during hyperbolic dehn filling the proofs involve the construction of a family of hyperbolic conemanifold structures using infinitesimal harmonic deformations and analysis of geometric limits

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

mixed finite elements for the richards equation linearization procedure we consider mixed finite element discretization for a class of degenerate parabolic problems including the richards equation after regularization time discretization is achieved by an euler implicit scheme while mixed finite elements are employed for the discretization in space based on the results obtained in radu et al rana preprint 02 06 eindhoven university of technology 2002 this paper considers a simple iterative scheme to solve the emerging nonlinear elliptic problems

dehn surgery on knots in d dehn considered the following method for constructing 3 manifolds remove a solid torus neighborhood n k of some knot x in the 3 sphere s and sew it back differently in particular he showed that taking x to be the trefoil one could obtain infinitely many non simply connected homology spheres o in this way let mx s n k then the different resewings are parametrized by the isotopy class r of the simple closed curve on the torus omk that bounds a meridional disk in the re attached solid torus we denote the resulting closed oriented 3 manifold by mk and say that it is obtained by r dehn surgery on x more generally one can consider the manifolds ml obtained by r dehn surgery on a fc component link l xi u u kk in s where r r it turns out that every closed oriented 3 manifold can be constructed in this way wal lie thus a good understanding of dehn surgery might lead to progress on general questions about the structure of 3 manifolds starting with the case of knots it is natural to extend the context a little and consider the manifolds m r obtained by attaching a solid torus v to an arbitrary compact oriented irreducible every 2 sphere bounds a 3 ball 3 manifold m with dm an incompressible torus where r is the isotopy class slope on dm of the boundary of a meridional disk of v we say that m r is the result of r dehn filling on m an observed feature of this construction is that

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

mixed finite element methods for linear elasticity with weakly imposed symmetry in this paper we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approxima tions to both stresses and displacements the methods are based on a modified form of the hellinger reissner variational principle that only weakly imposes the symmetry condition on the stresses although this approach has been previously used by a number of authors a key new ingredient here is a constructive derivation of the elasticity complex starting from the de rham complex by mimicking this construction in the discrete case we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de rham complex these elements appear to be simpler than the ones previously derived for example we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field

collisions of particles in locally ads spacetimes i local description and global examples we investigate 3 dimensional globally hyperbolic ads manifolds or more generally constant curvature lorentz manifolds containing particles i e cone singularities along a graph we impose physically relevant conditions on the cone singularities e g positivity of mass angle less than 2 on time like singular segments we construct examples of such manifolds describe the cone singularities that can arise and the way they can interact the local geometry near the vertices of we then adapt to this setting some notions like global hyperbolicity which are natural for lorentz manifolds and construct some examples of globally hyperbolic ads manifolds with interacting particles

cannon thurston maps for surface groups we prove the existence of cannon thurston maps for simply and doubly degenerate surface kleinian groups as a consequence we prove that connected limit sets of nitely generated kleinian groups are locally connected

quasi fuchsian manifolds with particles we consider 3 dimensional hyperbolic cone manifolds which are convex cocompact in a natural sense with cone singularities along infinite lines such singularities are sometimes used by physicists as models for massive spinless point particles we prove an infinitesimal rigidity statement when the angles around the singular lines are less than any infinitesimal deformation changes either these angles or the conformal structure at infinity with marked points corresponding to the endpoints of the singular lines moreover any small variation of the conformal structure at infinity and of the singular angles can be achieved by a unique small deformation of the cone manifold structure these results hold also when the singularities are along a graph i e for interacting particles

on the existence of orders in semisimple hopf algebras the first author was supported by the projects mtm2011 27090 from micinn and feder and by the research group fqm0211 from junta de andalucia the second author was supported by the danish national research foundation dnrf through the centre for symmetry and deformation the authors would like to thank dmitriy rumynin and martin lorenz for bring ing to their attention the notion of weak order cesar galindo for pointing out that these examples were already discussed in 8 and yevgenia kashina and sonia na tale for useful discussions on the classification of low dimensional semisimple hopf algebras

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

infinitesimal rigidity of cone manifolds and the stoker problem for hyperbolic and euclidean polyhedra the deformation theory of hyperbolic and euclidean cone manifolds with all cone angles less than 2 plays an important role in many problems in low dimensional topology and in the geometrization of 3 manifolds furthermore various old conjectures dating back to stoker about the moduli space of convex hyperbolic and euclidean polyhedra can be reduced to the study of deformations of cone manifolds by doubling a polyhedron across its faces this deformation theory has been understood by hodgson and kerckhoff 7 when the singular set has no vertices and by weis 32 when the cone angles are less than we prove here an infinitesimal rigidity result valid for cone angles less than 2 stating that infinitesimal deformations which leave the dihedral angles fixed are trivial in the hyperbolic case and reduce to some simple deformations in the euclidean case the method is to treat this as a problem concerning the deformation theory of singular einstein metrics and to apply analytic methods about elliptic operators on stratified spaces this work is an important ingredient in the local deformation theory of cone manifolds by the second author 22 see also the concurrent work by weis 33

crystal dissolution and precipitation in porous media pore scale analysis in this paper we discuss a pore scale model for crystal dissolution and precipitation in porous media we consider first general domains for which existence of weak solutions is proven for the particular case of strips we show that free boundaries occur in the form of dissolution precipitation fronts as the ratio between the thickness and the length of the strip vanishes we obtain the upscaled reactive solute transport model proposed in 12

semisimple hopf actions on commutative domains abstract let h be a semisimple so finite dimensional hopf algebra over an algebraically closed field k of characteristic zero and let a be a commutative domain over k we show that if a arises as an h module algebra via an inner faithful h action then h must be a group algebra this answers a question of e kirkman and j kuzmanovich and partially answers a question of m cohen the main results of this article extend to working over k of positive characteristic on the other hand we obtain results on hopf actions on weyl algebras as a consequence of the main theorem

word hyperbolic dehn surgery in the late 1970 s thurston dramatically changed the nature of 3 manifold theory with the introduction of his geometrisation conjecture and by proving it in the case of haken 3 manifolds 23 the conjecture for general closed orientable 3 manifolds remains perhaps the most important unsolved problem in the subject a weaker form of the conjecture 19 deals with the fundamental group of a closed orientable 3 manifold it proposes that either it contains z z as a subgroup or it is word hyperbolic in the sense of gromov 11 word hyperbolic groups are precisely those groups which satisfy a linear isoperimetric inequality they are of fundamental importance in geometric group theory and have very many useful properties

local rigidity of 3 dimensional cone manifolds we investigate the local deformation space of 3 dimensional conemanifold structures of constant curvature 1 0 1 and coneangles under this assumption on the cone angles the singular locus will be a trivalent graph in the hyperbolic and the spherical case our main result is a vanishing theorem for the first l 2 cohomology group of the smooth part of the cone manifold with coefficients in the flat bundle of infinitesimal isometries weconclude local rigidity from this in the euclidean case we prove that the first l 2 cohomology group of the smooth part with coefficients in the flat tangent bundle is represented by parallel forms

examples of relative deformation spaces that are not locally connected we provide an infinite family of pared manifolds with the property that the relative deformation spaces of hyperbolic structures on these manifolds are not locally connected this is a natural extension of the recent result of bromberg that shows the space of kleinian punctured torus groups is not locally connected