on witten s proof of the positive energy theorem this paper gives a mathematically rigorous proof of the positive energy theorem using spinors this completes and simplifies the original argument presented by edward witten we clarify the geometric aspects of this argument and prove the necessary analytic theorems concerning the relevant dirac operator

a positive mass theorem in three dimensional cauchy riemann geometry in this note we summarize the results from 6 on the positive mass problem in 3 dimensional cr cauchy riemann geometry

existence of maximal surfaces in asymptotically flat spacetimes we prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition this uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the dirichlet problem

on a spin conformal invariant on manifolds with boundary let m be an n dimensional connected compact manifold with non empty boundary equipped with a riemannian metric g a spin structure and a chirality operator we define and study some properties of a spin conformal invariant given by lambda rm min m partial m underset overline g in g rm inf lambda 1 pm overline g rm vol m overline g frac 1 n where lambda 1 pm overline g is the smallest eigenvalue of the dirac operator under the chiral bag boundary condition mathbb b pm overline g more precisely we show that if n 2 then lambda rm min m partial m leq lambda rm min mathbb s n partial mathbb s n

eigenvalue boundary problems for the dirac operator on a compact riemannian spin manifold with mean convex boundary we analyse the ellipticity and the symmetry of four boundary conditions for the fundamental dirac operator including the global aps condition and a riemannian version of the local mit bag condition we show that friedrich s inequality for the eigenvalues of the dirac operator on closed spin manifolds holds for the corresponding four eigenvalue boundary problems more precisely we prove that for both the aps and the mit conditions the equality cannot be achieved and for the other two conditions the equality characterizes respectively half spheres and domains bounded by minimal hypersurfaces in manifolds carrying non trivial real killing spinors

a penrose like inequality for the mass of riemannian asymptotically flat manifolds we prove an optimal penrose like inequality for the mass of any asymptotically flat riemannian 3 manifold having an inner minimal 2 sphere and nonnegative scalar curvature our result shows that the mass is bounded from below by an expression involving the area of the minimal sphere as in the original penrose conjecture and some nomalized sobolev ratio as expected the equality case is achieved if and only if the metric is that of a standard spacelike slice in the schwarzschild space

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

the weighted particle method for convection diffusion equations ii the anisotropic case on etend la methode particulaire utilisee dans la partie i pour les equations de convection diffusion aux operateurs de diffusion anisotrope des conditions plus complexes que dans le cas isotrope sont exigees pour les fonctions de cutoff une analyse d erreur detaillee est effectuee

universal positive mass theorems in this paper we develop a general study of contributions at infinity of bochner weitzenbock type formulas on asymptotically flat manifolds inspired by witten s proof of the positive mass theorem as an application we show that similar proofs can be obtained in a much more general setting as any choice of an irreducible natural bundle and a very large choice of first order operators may lead to a positive mass theorem along the same lines if the necessary curvature conditions are satisfied

on tiling under tomographic constraints given a tiling of a 2d grid with several types of tiles we can count for every row and column how many tiles of each type it intersects these numbers are called the projections we are interested in the problem of reconstructing a tiling which has given projections some simple variants of this problem involving tiles that are 1 1 or 1 2 rectangles have been studied in the past and were proved to be either solvable in polynomial time or np complete in this note we make progress toward a comprehensive classification of various tiling reconstruction problems by proving np completeness results for several sets of tiles

a strictly positive mass theorem we show that the adm 4 momentum of an isolated gravitational system spatially asymptotically flat spacetime satisfying the dominant energy condition cannot be null like unless it is flat together with the positive mass theorem this implies that the adm 4 momentum of an isolated gravitational system must be strictly time like

positivity of quasi local mass ii a spacetime is a four manifold with a pseudo metric of signature a hypersurface or a 2 surface in a spacetime is spacelike if the induced metric is pos itive definite a quasi local energy momentum vector is a vector in r3 1 associated to a spacelike 2 surface which depends on its first and second fundamental forms and the connection to its normal bundle in the spacetime the time component of the four vector is called quasi local energy mass similar to 10 8 we require the quasi local energy momentum vector to satisfy the following properties 1 it should be zero for the flat spacetime 2 the quasi local mass should be equivalent to the standard definition if the spacetime is spherically symmetric and the quasi local mass is evaluated on the spheres 7 we say that two masses mi and m2 are equivalent if there is a universal constant c 0 such that c lm area e 167r 6 the quasi local energy momentum vector should be nonspacelike and the quasi local mass should be nonnegative

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

monopoles on asymptotically euclidean 3 manifolds on considere une generalisation de la theorie de yang mills higgs sur r 3 euclidien a des sommes convexes de r 3 avec des 3 varietes closes compactes

monopoles and maps from s 2 to s 2 the topology of the configuration space the configuration space for the su 2 yang mills higgs equations on 3 is shown to be homotopic to the space of smooth maps froms 2 tos 2 this configuration space indexes a family of twisted dirac operators the dirac family is used to prove that the configuration space does not retract onto any subspace on which the su 2 yang mills higgs functional is bounded

extrinsic killing spinors under intrinsic and extrinsic curvature assumptions on a riemannian spin manifold and its boundary we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic killing spinors of non negative killing constant as a corollary we prove that a complete ricci flat spin manifold with mean convex boundary isometric to a round sphere is necessarily a flat disc

equivalence of the spinor and tensor methods in the positive energy problem we prove that nontrivial solutions of the sen witten equation with asymptotically flat data set on maximal hypersurface does not equal zero at any point of this hypersurface on this basis we ascertain the equivalence of witten s spinor method and nester s tensor method in the positive energy problem in general relativity

a note on positive energy theorem for spaces with asymptotic susy compactification we extend the higher dimensional positive mass theorem in dai x commun math phys 244 335 345 2004 to the lorentzian setting this includes the original higher dimensional positive energy theorem whose spinor proof is given in witten e commun math phys 80 381 402 1981 and parker t and taubes c commun math phys 84 223 238 1982 for dimension 4 and in zhang x j math phys 40 3540 3552 1999 for dimension 5

deformations of the hemisphere that increase scalar curvature consider a compact riemannian manifold m of dimension n whose boundary m is totally geodesic and is isometric to the standard sphere s n 1 a natural conjecture of min oo asserts that if the scalar curvature of m is at least n n 1 then m is isometric to the hemisphere s n equipped with its standard metric this conjecture is inspired by the positive mass theorem in general relativity and has been verified in many special cases in this paper we construct counterexamples to min oo s conjecture in dimension n 3

a conformal lower bound for the smallest eigenvalue of the dirac operator and killing spinors on a riemannian spin manifold we give a lower bound for the square of the eigenvalues of the dirac operator by the smallest eigenvalue of the conformal laplacian the yamabe operator we prove in the limiting case that the eigenspinor field is a killing spinor i e parallel with respect to a natural connection in particular if the scalar curvature is positive the eigenspinor field is annihilated by harmonic forms and the metric is einstein

a tiling system for the class of l convex polyominoes a polyomino is said to be l convex if any two of its cells can be connected by a path entirely contained in the polyomino and having at most one change of direction in this paper answering a problem posed by castiglione and vaglica 6 we prove that the class of l convex polyominoes is tiling recognizable to reach this goal first we express the l convexity constraint in terms of a set of independent properties then we show that each class of convex polyominoes having one of these properties is tiling recognizable

reconstructing convex polyominoes from horizontal and vertical projections in 1 we studied the problem of reconstructing a discrete set 5 from its horizontal and vertical projections we defined an algorithm that establishes the existence of a convex polyomino whose horizontal and vertical projections are equal to a pair of assigned vectors h v with h m and v n its computational cost is o n4m4 in this paper we introduce some operations for recontructing convex polyominoes by means of vectors h s and v s partial sums these operations allows us to define a new algorithm whose complexity is less than o n2m2

a volterra type model for image processing we present a class of time delay anisotropic diffusion models for image restoration these models lead to asymptotic states that are selected on the basis of a contrast parameter and bear some analogy with neural networks with hebbian dynamical learning rules numerical examples show that these models are efficient in removing even high levels of noise while allowing an accurate tracking of the edges

a definition of total energy momenta and the positive mass theorem on asymptotically hyperbolic 3 manifolds i two sets of asymptotically hyperbolic initial data are defined which correspond to the spatial infinity in asymptotically ads spacetimes and to the null infinity in asymptotically minkowski spacetimes respectively the positive mass theorem involving the total energy the total linear momentum and the total angular momentum is established for these initial data sets

reconstruction of convex polyominoes with a blocking component several papers in the available literature tackled problems concerning convex polyominoes in discrete tomography an interesting subclass consists of l convex polyominoes since the related reconstruction problem can have only a unique solution on the other hand recent studies have modeled an approach to reconstruct objects even in the case that some of the projections are unavailable due to a particularly dense part of the scanned object that we refer to as a blocking component in this work we merge the two problems in order to obtain efficient reconstruction algorithms for convex and l convex polyominoes in case a blocking component is included

the analysis of partial differential operators i hormander springer 1985 vol 1 391 pp vol 2 390 pp vol 3 525 pp vol 4 351 pp

moduli spaces of self dual connections over asymptotically locally flat gravitational instantons we investigate yang mills instanton theory over four dimensional asymptotically locally flat alf geometries including gravitational instantons of this type by exploiting the existence of a natural smooth compactification of these spaces introduced by hausel hunsicker mazzeo first referring to the codimension 2 singularity removal theorem of sibner sibner and rade we prove that given a smooth finite energy self dual su 2 connection over a complete alf space its energy is congruent to a chern simons invariant of the boundary three manifold if the connection satisfies a certain holonomy condition at infinity and its curvature decays rapidly then we introduce framed moduli spaces of self dual connections over ricci flat alf spaces we prove that the moduli space of smooth irreducible rapidly decaying self dual connections obeying the holonomy condition with fixed finite energy and prescribed asymptotic behaviour on a fixed bundle is a finite dimensional manifold we calculate its dimension by a variant of the gromov lawson relative index theorem as an application we study yang mills instantons over the flat mathbb r 3 times s 1 the multi taub nut family and the riemannian schwarzschild space

determinants of dirac operators with local boundary conditions we study functional determinants for dirac operators on manifolds with boundary we give for local boundary conditions an explicit formula relating these determinants to the corresponding green s functions we finally apply this result to the case of a bidimensional disk under baglike conditions

energy quantization for a singular super liouville boundary value problem in this paper we develop the blow up analysis and establish the energy quantization for solutions to super liouville type equations on riemann surfaces with conical singularities at the boundary in other problems in geometric analysis the blow up analysis usually strongly utilizes conformal invariance which yields a noether current from which strong estimates can be derived here however the conical singularities destroy conformal invariance therefore we develop another more general method that uses the vanishing of the pohozaev constant for such solutions to deduce the removability of boundary singularities

positive mass theorem and the boundary behaviors of compact manifolds with nonnegative scalar curvature in this paper we study the boundary behaviors of compact manifolds with nonnegative scalar curvature and nonempty boundary using a general version of positive mass theorem of schoen yau and witten we prove the following theorem for any compact manifold with boundary and nonnegative scalar curvature if it is spin and its boundary can be isometrically embedded into euclidean space as a strictly convex hypersurface then the integral of mean curvature of the boundary of the manifold cannot be greater than the integral of mean curvature of the embedded image as a hypersurface in euclidean space moreover equality holds if and only if the manifold is isometric with a domain in the euclidean space conversely under the assumption that the theorem is true then one can prove the adm mass of an asymptotically flat manifold is nonnegative which is part of the positive mass theorem

the mass of an asymptotically flat manifold we show that the mass of an asymptotically flat n manifold is a geometric invariant the proof is based on harmonic coordinates and to develop a suitable existence theory results about elliptic operators with rough coefficients on weighted sobolev spaces are summarised some relations between the mass scalar curvature and harmonic maps are described and the positive mass theorem for n dimensional spin manifolds is proved

killing vectors in asymptotically flat space times ii asymptotically translational killing vectors and the rigid positive energy theorem in higher dimensions we show that the borderline cases in the proof of the positive energy theorem for initial data sets on spin manifolds in dimensions n 3 are only possible for initial data arising from embeddings in minkowski space time

spectral triples and manifolds with boundary abstract we investigate manifolds with boundary in noncommutative geometry spectral triples associated to a symmetric differential operator and a local boundary condition are constructed we show that there is no tadpole for classical dirac operators with a chiral boundary condition on spin manifolds

positive mass conjecture for five dimensional lorentzian manifolds we extend witten s proof on positive mass conjecture to five dimensional lorentzian manifolds with a rigorous treatment in mathematics

scalar curvature and hammocks scalar curvature is the simplest generalization of gaussian curvature to higher dimensions however there are many questions open with regard to its relation to other geometric quantities and topology here we will prove and illustrate some features of scalar curvature in higher dimensions related to a general hammock effect for scalar curvature namely the one sided affinity for curvature decreasing deformations the first one is concerned with some prescribed decrease of the scalar curvature scal g of some riemannian metric g on a given manifoldmn of dimension 3 we denote the e neighborhood of some set u with respect to g by ue

on the positive energy theorem involving mass and electromagnetic charges a new theorem relating mass and charges is deduced which can be applied to more general physical systems than those covered by the theorem of gibbons and hull 1

a backward forward regularization of the perona malik equation abstract it is shown that the perona malik equation pme admits a natural regularization by forward backward diffusions possessing better analytical properties than pme itself well posedness of the regularizing problem along with a complete understanding of its long time behavior can be obtained by resorting to weak young measure valued solutions in the spirit of kinderlehrer and pedregal 1992 1 and demoulini 1996 2 solutions are unique to an extent to be specified but can exhibit micro oscillations in the sense of minimizing sequences and in the spirit of material science between preferred gradient states in the limit of vanishing regularization the preferred gradients have size 0 or thus explaining the well known phenomenon of staircasing the theoretical results do completely confirm and or predict numerical observations concerning the generic behavior of solutions

the classification of static electro vacuum space times containing an asymptotically flat spacelike hypersurface with compact interior we show that static electro vacuum black hole space times containing an asymptotically flat spacelike hypersurface with compact interior and with both degenerate and non degenerate components of the event horizon do not exist this is done by a careful study of the near horizon geometry of degenerate horizons which allows us to eliminate the last restriction of the static electro vacuum no hair theory

killing vectors in asymptotically flat space times i asymptotically translational killing vectors and the rigid positive energy theorem we study killing vector fields in asymptotically flat space times we prove the following result implicitly assumed in the uniqueness theory of stationary black holes if the conditions of the rigidity part of the positive energy theorem are met then in such space times there are no asymptotically null killing vector fields except if the initial data set can be embedded in minkowski space time we also give a proof of the nonexistence of nonsingular in an appropriate sense asymptotically flat space times that satisfy an energy condition and that have a null adm four momentum under conditions weaker than previously considered

a new mass for asymptotically flat manifolds abstract in this paper we introduce a mass for asymptotically flat manifolds by using the gauss bonnet curvature we first prove that the mass is well defined and is a geometric invariant if the gauss bonnet curvature is integrable and the decay order satisfies n 4 3 motivated by an elegant idea of lam 35 we then show a positive mass theorem for this new mass for asymptotically flat graphs over r n moreover we obtain various penrose type inequalities in this case in these penrose type inequalities we establish relationship between the new mass and various geometric integrals

real killing spinors and holonomy we give a description of all complete simply connected riemannian manifolds carrying real killing spinors furthermore we present a construction method for manifolds with the exceptional holonomy groupsg2 and spin 7

proof of the positive mass theorem ii the positive mass theorem states that for a nontrivial isolated physical system the total energy which includes contributions from both matter and gravitation is positive this assertion was demonstrated in our previous paper in the important case when the space time admits a maximal slice here this assumption is removed and the general theorem is demonstrated abstracts of the results of this paper appeared in 11 and 13

a trace formula for dirac green s functions related by darboux transformations we construct green s functions and a trace formula for pairs of stationary dirac equations under sturm liouville boundary conditions where the equations are related to each other by a darboux transformation our findings generalize former results pozdeeva e 2008 j phys a math theor at press

eigenvalue estimate of the dirac operator and rigidity of poincare einstein metrics we re visit the eigenvalue estimate of the dirac operator on spin manifolds with boundary in terms of the first eigenvalues of conformal laplace operator as well as the conformal mean curvature operator these problems were studied earlier by hijazi montiel zhang and raulot and we re prove them under weaker assumption that a boundary chirality operator exists moreover on these spin manifolds with boundary we show that any c 3 alpha conformal compactification of some poincare einstein metric must be the standard hemisphere when the first nonzero eigenvalue of the dirac operator achieves its lowest value and any c 3 alpha conformal compactification of some poincare einstein metric must be the flat ball in euclidean space when the first positive eigenvalue of the boundary dirac operator achieves certain value relating to the second yamabe invariant in two cases the poincare einstein metrics are standard hyperbolic metric

a family of asymptotically hyperbolic manifolds with arbitrary energy momentum vectors a family of non radial solutions to the yamabe equation modeled on the hyperbolic space is constructed using power series as a result we obtain a family of asymptotically hyperbolic metrics with spherical conformal infinity with scalar curvature greater than or equal to n n 1 but which are a priori not complete moreover any vector of rn 1 is performed by an energy momentun vector of one suitable metric of this family they can in particular provide counter examples to the positive energy momentum theorem when one removes the completeness assumption

scalar curvature rigidity of asymptotically hyperbolic spin manifolds in this paper we study the hyperbolic version of this result using witten s method and show that a spin manifold which is strongly asymptotically hyperbolic cannot have scalar curvature r n n 1 everywhere unless it is isometric to hyperbolic space

positive mass theorems for higher dimensional lorentzian manifolds we extend witten s proof a new proof of the positive energy theorem commun math phys 80 381 402 1981 of the positive mass theorem to a rigorous proof for lorentzian manifolds of any dimension this includes the original higher dimensional positive mass theorem proved by spinors parker t and taubes c on witten s proof of the positive energy theorem commun math phys 84 223 238 1982 for dimension 4 and zhang x positive mass conjecture for five dimensional lorentzian manifolds j math phys 40 3540 3552 1999 for dimension 5 stimulated by the article of zhang positive mass theorem for hypersurface in 5 dimensional lorentzian manifolds commun anal geom 8 635 652 2000 we weaken the spin condition on the spacelike hypersurface to require only a spinc structure and give a modified positive mass theorem for lorentzian manifolds for dimensions 4 5 and 6

yamabe flow and adm mass on asymptotically flat manifolds in this paper we investigate the behavior of adm mass and einstein hilbert functional under the yamabe flow through studying the yamabe flow by weighted spaces for parabolic operators we show that the asymptotically flat property is preserved under the yamabe flow we also obtain that adm mass is invariant under the yamabe flow and yamabe flow is the gradient flow of einstein hilbert functional on n dimensional n 3 asymptotically flat manifolds with order n 22 for n 3 4 or n 3 for n 4 moreover we show that adm mass and einstein hilbert functional are non increasing under the yamabe flow on n dimensional asymptotically flat manifolds if we only assume the order n 22 for n 4

a positive mass theorem for spaces with asymptotic susy compactification we prove a positive mass theorem for spaces which asymptotically approach a flat euclidean space times a calabi yau manifold or any special honolomy manifold except the quaternionic kahler this is motivated by the very recent work of hertog horowitz maeda hhm

stability in yang mills theories at a solution of the yang mills equations ons4 or the yang mills higgs equation on 3 the hessian of the action functional defines a natural second order elliptic operator the number of negative eigenvalues of this operator is bounded below by a multiple of the relevant topological charge the proof of this assertion requires a relative index theorem for dirac type operators on n n 3

the gbc mass for asymptotically hyperbolic manifolds the paper consists of two parts in the first part by using the gauss bonnet curvature which is a natural generalization of the scalar curvature we introduce a higher order mass the gauss bonnet chern mass m mathbb h k for asymptotically hyperbolic manifolds and show that it is a geometric invariant moreover we prove a positive mass theorem for this new mass for asymptotically hyperbolic graphs and establish a relationship between the corresponding penrose type inequality for this mass and weighted alexandrov fenchel inequalities in the hyperbolic space mathbb h n in the second part we establish these weighted alexandrov fenchel inequalities in mathbb h n for any horospherical convex hypersurface sigma begin aligned int sigma v sigma 2k 1 d mu ge c n 1 2k 1 omega n 1 left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned where sigma j is the j th mean curvature of sigma subset mathbb h n v cosh r and sigma is the area of sigma as an application we obtain an optimal penrose type inequality for the new mass defined in the first part begin aligned m k mathbb h ge frac 1 2 k left left frac sigma omega n 1 right frac n k n 1 left frac sigma omega n 1 right frac n 2k k n 1 right k end aligned for asymptotically hyperbolic graphs with a horizon type boundary sigma provided that a dominant energy type condition tilde l k ge 0 holds both inequalities are optimal

equality in the spacetime positive mass theorem we affirm the rigidity conjecture of the spacetime positive mass theorem in dimensions less than eight namely if an asymptotically flat initial data set satisfies the dominant energy condition and has e p then e p 0 where e p is the adm energy momentum vector the dimensional restriction can be removed if we assume the positive mass inequality holds previously the result was only known for spin manifolds beig and chru ciel in j math phys37 4 1939 1961 1996 chru ciel and maerten in j math phys 47 2 2006

the positive mass theorem for manifolds with distributional curvature we formulate and prove a positive mass theorem for n dimensional spin manifolds whose metrics have only the sobolev regularity c 0 cap w rm loc 1 n at this level of regularity the curvature of the metric is defined in the distributional sense only and we propose here a generalized notion of adm mass for such a metric our main theorem establishes that if the manifold is asymptotically flat and has non negative scalar curvature distribution then its generalized adm mass is well defined and non negative and vanishes only if the manifold is isometric to euclidian space prior applications of witten s spinor method by lee and parker and by bartnik required the much stronger regularity w rm loc 2 p with p n our proof is a generalization of witten s arguments in which we must treat the dirac operator and its associated lichnerowicz weitzenbock identity in the distributional sense and cope with certain averages of first order derivatives of the metric over annuli that approach infinity finally we observe that our arguments are not specific to scalar curvature and also allow us to establish a universal positive mass theorem

a simple proof of the positivity of the bondi mass using a nonsingular hypersurface that is not only asymptotically null the authors prove the existence of spinor fields that yield a positive expression for the bondi mass standard existence theorems based on compact hypersurfaces are applied

combined curvelet shrinkage and nonlinear anisotropic diffusion in this paper a diffusion based curvelet shrinkage is proposed for discontinuity preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme in order to suppress the pseudo gibbs and curvelet like artifacts the conventional shrinkage results are further processed by a projected total variation diffusion in which only the insignificant curvelet coefficients or high frequency part of the signal are changed by use of a constrained projection numerical experiments from piecewise smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components in comparison to some existing methods

asymptotically flat conformal structures in the first part of this paper we revisit the theory of weighted spinors on conformal manifolds in the second part we introduce the notions of asymptotically flat weyl structures and of associated mass and we prove a conformal version of the positive mass theorem on conformal spin manifolds

conjugacy relationship between m convex and l convex functions in continuous variables by extracting combinatorial structures in well solved nonlinear combinatorial optimization problems murota 1996 1998 introduced the concepts of m convexity and l convexity to functions defined over the integer lattice recently murota shioura 2000 2001 extended these concepts to polyhedral convex functions and quadratic functions in continuous variables in this paper we consider a further extension to more general convex functions defined over the real space and provide a proof for the conjugacy relationship between general m convex and l convex functions

gauge choice in witten s energy expression witten s equation not d psi 0 can be interpreted as a gauge fixing condition for classical supergravity we rigorously prove the existence of asymptotically constant solutions of the more general gauge condition not d psi a psi for almost all endomorphismsa of the spin bundle each gives an expression for the gravitational energy similar to witten s these include the choice a sqrt r which yields the particularly elegant energy expression first noticed by deser

the dirac witten operator on pseudo riemannian manifolds we study the dirac witten operator for spacelike spin submanifolds in pseudo riemannian manifolds when the normal bundles are spin and odd dimensional we derive new eigenvalue lower bounds we also prove the generalized positive mass theorem using this operator

a new nonlocal nonlinear diffusion of image processing abstract a novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing the equation can be viewed as a new paradigm for the regularization of the well known perona malik equation the regularization is implemented via nonlinearity intensity reduction through fractional derivatives well posedness in the weak setting is established global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of perona malik

chern s magic form and the gauss bonnet chern mass in this note we use chern s magic form phi k in his famous proof of the gauss bonnet theorem to define a mass for asymptotically flat manifolds it turns out that the new defined mass is equivalent to the one that we introduced recently by using the gauss bonnet chern curvature l k moreover this equivalence implies a simple proof of the equivalence between the adm mass and the intrinsically defined mass via the ricci tensor which was reconsidered by miao tam proc am math soc 144 753 761 2016 and herzlich ann henri poincare 17 12 3605 3617 2016 very recently

lower eigenvalue estimates for dirac operators we derive upper eigenvalue estimates for generalized dirac operators on closed riemannian manifolds in the case of the classical dirac operator the estimates on the first eigenvalues are sharp for spheres of constant curvature

remarks on positive mass theorem we establish a positive mass theorem for time symmetric initial data sets by relaxing the nonnegative scalar curvature to the case where the first neumann eigenvalue of conformal laplacian operators is eventually nonnegative

anisotropic diffusion filter with memory based on speckle statistics for ultrasound images ultrasound us imaging exhibits considerable difficulties for medical visual inspection and for development of automatic analysis methods due to speckle which negatively affects the perception of tissue boundaries and the performance of automatic segmentation methods with the aim of alleviating the effect of speckle many filtering techniques are usually considered as a preprocessing step prior to automatic analysis methods or visual inspection most of the state of the art filters try to reduce the speckle effect without considering its relevance for the characterization of tissue nature however the speckle phenomenon is the inherent response of echo signals in tissues and can provide important features for clinical purposes this loss of information is even magnified due to the iterative process of some speckle filters e g diffusion filters which tend to produce over filtering because of the progressive loss of relevant information for diagnostic purposes during the diffusion process in this paper we propose an anisotropic diffusion filter with a probabilistic driven memory mechanism to overcome the over filtering problem by following a tissue selective philosophy in particular we formulate the memory mechanism as a delay differential equation for the diffusion tensor whose behavior depends on the statistics of the tissues by accelerating the diffusion process in meaningless regions and including the memory effect in regions where relevant details should be preserved results both in synthetic and real us images support the inclusion of the probabilistic memory mechanism for maintaining clinical relevant structures which are removed by the state of the art filters

total mass momentum of arbitrary initial data sets in general relativity for an asymptotically flat initial data set in general relativity the total mass momentum may be interpreted as a hermitian quadratic form on the complex two dimensional vector space of asymptotic spinors a generalization to an arbitrary initial data set is obtained the mass momentum is retained as a hermitian quadratic form but the space of asymptotic spinors on which it is a function is modified indeed the dimension of this space may range from zero to infinity depending on the initial data there is given a variety of examples and general properties of this generalized mass momentum

proof of the riemannian penrose inequality using the positive mass theorem we prove the riemannian penrose conjecture an important case of a con jecture 41 made by roger penrose in 1973 by defining a new flow of metrics this flow of metrics stays inside the class of asymptotically flat riemannian 3 manifolds with nonnegative scalar curvature which contain minimal spheres in particular if we consider a riemannian 3 manifold as a totally geodesic submanifold of a space time in the context of general relativity then outermost minimal spheres with total area a correspond to apparent horizons of black holes contributing a massa 16 scalar cur vature corresponds to local energy density at each point and the rate at which the metric becomes flat at infinity corresponds to total mass also called the adm mass the riemannian penrose conjecture then states that the total mass of an asymptotically flat 3 manifold with nonnegative scalar curvature is greater than or equal to the mass contributed by the black holes the flow of metrics we define continuously evolves the original 3 metric to a schwarzschild 3 metric which represents a spherically symmetric black hole in vacuum we define the flow such that the area of the minimal spheres which flow outward and hence the mass contributed by the black holes in each of the metrics in the flow is constant and then use the positive mass theorem to show that the total mass of the metrics is nonincreasing then since the total mass equals the mass of the black hole in a schwarzschild metric the riemannian penrose conjecture follows we also refer the reader to the beautiful work of huisken and ilmanen 30 who used inverse mean curvature flows of surfaces to prove that the total mass is at least the mass contributed by the largest black hole in sections 1 and 2 we motivate the problem discuss important quantities like total mass and horizons of black holes and state the positive mass theorem and the penrose conjecture for riemannian 3 manifolds in section 3 we give the proof of the riemannian penrose

homothetic and conformal symmetries of solutions to einstein s equations we present several results about the nonexistence of solutions of einstein s equations with homothetic or conformal symmetry we show that the only spatially compact globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature and also admitting an infinitesimal proper homothetic symmetry are everywhere locally flat this assumes that the matter fields either obey certain energy conditions or are the yang mills or massless klein gordon fields we find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions we show that if the dominant energy condition is assumed then minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation in other words with the exceptions cited homothetic or conformal killing fields are in fact killing in spatially compact or asymptotically flat spactimes in the conformal procedure for solving the initial value problem we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry