asymptotic behavior of solutions of second order differential equations with integrable coefficients the differential equation x a t f x 0 t 0 is considered under the condition that lim x fl a s ds exists and is finite and necessary and or sufficient conditions are given for this equation to have solutions which behave asymptotically like nontrivial linear functions cl c2t

a renorming in some banach spaces with applications to fixed point theory abstract we consider a banach space x endowed with a linear topology and a family of seminorms r k which satisfy some special conditions we define an equivalent norm on x such that if c is a convex bounded closed subset of x which is relatively sequentially compact then every nonexpansive mapping t c c has a fixed point as a consequence we prove that if g is a separable compact group its fourier stieltjes algebra b g can be renormed to satisfy the fpp in case that g t we recover p k lin s renorming in the sequence space l 1 moreover we give new norms in l 1 with the fpp we find new classes of nonreflexive banach spaces with the fpp and we give a sufficient condition so that a nonreflexive subspace of l 1 can be renormed to have the fpp

monotone positive solutions of second order nonlinear differential equations we obtain an existence theorem for monotone positive solutions of nonlinear second order ordinary differential equations by using the schauder tikhonov fixed point theorem the result can also be applied to prove the existence of positive solutions of certain semilinear elliptic equations in r n n greater than or equal to 3

fourier stieltjes algebras and measure algebras on compact right topological groups abstract let g be an admissible compact hausdorff right topological group that is a group with a hausdorff topology such that for each a g the map g g a is continuous and the set of a g such that the map g a g is continuous is dense in g such groups arise in the study of distal flows in this paper we study the fourier stieltjes algebra b g the linear span of the continuous positive definite functions on g we show that b g is isomorphic with the fourier stieltjes algebra of an associated compact topological group this result is then applied to obtain some geometric properties including the weak and weak fixed point properties on b g we also study some related properties on the measure algebra m g

renormings and the fixed point property in non commutative l1 spaces abstract let m be a finite von neumann algebra it is known that l 1 m and every non reflexive subspace of l 1 m fail to have the fixed point property for non expansive mappings fpp we prove a new fixed point theorem for this class of mappings in non commutative l 1 m banach spaces which lets us obtain a sufficient condition such that a closed subspace of l 1 m can be renormed to satisfy the fpp as a consequence we deduce that the predual of every atomic finite von neumann algebra can be renormed with the fpp

a characterization of convex hyperbolic polyhedra and of convex polyhedra inscribed in the sphere we describe a characterization of convex polyhedra in h 3 in terms of their dihedral angles developed by rivin we also describe some geometric and combinatorial consequences of that theory one of these consequences is a combinatorial characterization of convex polyhedra in e 3 all of whose vertices lie on the unit sphere that resolves a problem posed by jakob steiner in 1832

on the renormalized volume of hyperbolic 3 manifolds the renormalized volume of hyperbolic manifolds is a quantity motivated by the ads cft correspondence of string theory and computed via a certain regularization procedure the main aim of the present paper is to elucidate its geometrical meaning we use another regularization procedure based on surfaces equidistant to a given convex surface n the renormalized volume computed via this procedure is equal to what we call the w volume of the convex region n given by the usual volume of n minus the quarter of the integral of the mean curvature over n the w volume satisfies some remarkable properties first this quantity is self dual in the sense explained in the paper second it verifies some simple variational formulas analogous to the classical geometrical schlafli identities these variational formulas are invariant under a certain transformation that replaces the data at n by those at infinity of m we use the variational formulas in terms of the data at infinity to give a simple geometrical proof of results of takhtajan et al on the kahler potential on various moduli spaces

fixed point properties and proximinality in banach spaces abstract in this paper we prove the existence of a fixed point for several classes of mappings mappings admitting a center nonexpansive mappings asymptotically nonexpansive mappings defined on the closed convex subsets of a banach space satisfying some proximinality conditions in particular we derive a sufficient condition more general than weak star compactness such that if c is a bounded closed convex subset of l 1 satisfying this condition then every nonexpansive mapping t c c has a fixed point

there is an equivalent norm on l1 that has the fixed point property abstract let k 8 k 1 8 k for all k n and let be the equivalent norm of l 1 defined by a n sup k n k n k a n for all x a n l 1 we prove that l 1 has the fixed point property for nonexpansive self mappings

homology of the configuration spaces of quasi equilateral polygon linkages we consider the configuration space mn r of quasi equilateral polygon linkages with n vertices each edge having length 1 except for one fixed edge having length r r 0 in the euclidean plane r2 in this paper we determine h mn r z

failure of the fpp inside an asymptotically isometric free copy of c0 abstract we produce an equivalent renorming of c 0 which fails to contain an asymptotically isometric copy of c 0 yet all of its infinite dimensional subspaces fail to have the fixed point property for nonexpansive mappings on closed bounded convex subsets

renorming of l1 and the fixed point property abstract for any k n let p k denote the natural projections on l 1 let be an equivalent norm of l 1 that satisfies all of the following four conditions 1 there are 4 and a positive decreasing sequence n in 0 1 such that for any normalized block basis f n of l 1 and x l 1 with p k 1 x x and x k lim sup n f n x 1 x 2 there are two strictly decreasing sequences k and k with lim k k 0 and lim k k 1 such that for any normalized block basis f n of l 1 and x with i p k x x lim inf n f n x 1 k k 1 x 3 for any k n i p k 1 4 the unit ball of l 1 is l 1 c 0 closed in this article we prove that the space l 1 has the fixed point property for the nonexpansive mapping this improves a previous result of the author

on the teichmuller theory of circle patterns given a circle pattern on the riemann sphere in this paper we prove that its quasiconformal deformation space can be naturally identified with the product of the teichmuller spaces of its interstices

homoclinic orbits and subharmonics for nonlinear second order difference equations abstract we show the existence of a nontrivial homoclinic orbit and subharmonic solutions for a class of second order difference equations by applying the mountain pass theorem relying on ekeland s variational principle and the diagonal method and the homoclinic orbit as the limit of the subharmonics a completely new way is provided for dealing with the existence of solutions for difference equations

asymptotically isometric copies ofc0in banach spaces abstract if is an uncountable set then any equivalent renorming of c 0 contains an asymptotically isometric copy of c 0 if y is an infinite dimensional closed subspace of c 0 then y contains an asymptotically isometric copy of c 0 if x and y are two infinite dimensional banach spaces and if x contains an asymptotically isometric copy of c 0 then the injective tensor product of x and y x e y contains a complemented asymptotically isometric copy of c 0 similarly if x contains an asymptotically isometric copy of c 0 then the lebesgue bochner space l p 0 1 x contains a complemented asymptotically isometric copy of c 0

near infinity concentrated norms and the fixed point property for nonexpansive maps on closed bounded convex sets abstract in this paper we define the concept of a near infinity concentrated norm on a banach space x with a boundedly complete schauder basis when is such a norm we prove that x has the fixed point property fpp that is every nonexpansive self mapping defined on a closed bounded convex subset has a fixed point in particular p k lin s norm in l 1 14 and the norm p with p p n and lim n p n 1 introduced in 3 are examples of near infinity concentrated norms when p is equivalent to the l 1 norm it was an open problem as to whether l 1 p had the fpp we prove that the norm p always generates a nonreflexive banach space x r p 1 r p 2 r p 3 satisfying the fpp regardless of whether p is equivalent to the l 1 norm we also obtain some stability results

renormings of c0 and the fixed point property it is unknown whether all renormings of c0 fail the fixed point property fpp or not in this note we give a sufficient condition for a renorming of c0 to fail the fpp which is more general than the previously known ones in fact the condition is satisfied for all renormings of c0 we know it also allows us to show that for some usual renormings of c0 not only the whole space but all its infinite dimensional subspaces fail the fpp

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

gauss images of hyperbolic cusps with convex polyhedral boundary we prove that a 3 dimensional hyperbolic cusp with convex poly hedral boundary is uniquely determined by its gauss image furthermore any spherical metric on the torus with cone singularities of negative curvature and all closed contractible geodesics of length greater than 2 is the metric of the gauss image of some convex polyhedral cusp this result is an analog of the rivin hodgson theorem characterizing compact convex hyperbolic polyhedra in terms of their gauss images the proof uses a variational method namely a cusp with a given gauss image is identified with a critical point of a functional on the space of cusps with cone type singularities along a family of half lines the functional is shown to be concave and to attain maximum at an interior point of its domain as a byproduct we prove rigidity statements with respect to the gauss image for cusps with or without cone type singularities in a special case our theorem is equivalent to existence of a circle pattern on the torus with prescribed combinatorics and intersection angles this is the genus one case of a theorem by thurston in fact our theorem extends thurston s theorem in the same way as rivin hodgson s theorem extends an dreev s theorem on compact convex polyhedra with non obtuse dihedral angles the functional used in the proof is the sum of a volume term and curvature term we show that in the situation of thurston s theorem it is the potential for the combinatorial ricci flow considered by chow and luo our theorem represents the last special case of a general statement about isometric immersions of compact surfaces

a fixed point characterization of weak compactness in banach spaces with unconditional schauder basis abstract let x be a banach space with an 1 unconditional schauder basis and without isomorphic copies of l 1 c 0 we obtain an equivalent condition to weak compactness by means of a fixed point theorem namely a closed convex bounded subset c of x is weakly compact if and only if every cascading nonexpansive mapping t c c has a fixed point we particularize our results when c is the closed unit ball of the banach space x obtaining a new characterization of reflexivity note that weak compactness is independent of the underlying equivalent norm and that every banach space with an unconditional schauder basis can be renormed to be 1 unconditional

polyhedra inscribed in a quadric we study convex polyhedra in three space that are inscribed in a quadric surface up to projective transformations there are three such surfaces the sphere the hyperboloid and the cylinder our main result is that a planar graph gamma is realized as the 1 skeleton of a polyhedron inscribed in the hyperboloid or cylinder if and only if gamma is realized as the 1 skeleton of a polyhedron inscribed in the sphere and gamma admits a hamiltonian cycle this answers a question asked by steiner in 1832 rivin characterized convex polyhedra inscribed in the sphere by studying the geometry of ideal polyhedra in hyperbolic space we study the case of the hyperboloid and the cylinder by parameterizing the space of convex ideal polyhedra in anti de sitter geometry and in half pipe geometry just as the cylinder can be seen as a degeneration of the sphere and the hyperboloid half pipe geometry is naturally a limit of both hyperbolic and anti de sitter geometry we promote a unified point of view to the study of the three cases throughout

asymptotic to polynomials solutions for nonlinear differential equations abstract this article is concerned with solutions that behave asymptotically like polynomials for nth order n 1 nonlinear ordinary differential equations for each given integer m with 1 m n 1 sufficient conditions are presented in order that for any real polynomial of degree at most m there exists a solution which is asymptotic at to this polynomial conditions are also given which are sufficient for every solution to be asymptotic at to a real polynomial of degree at most n 1 the application of the results obtained to the special case of second order nonlinear differential equations leads to improved versions of the ones contained in the recent paper by lipovan glasg math j 45 2003 179 and of other related results existing in the literature

geometrization of 3 dimensional orbifolds this paper is devoted to the proof of the orbifold theorem if o is a compact connected orientable irreducible and topologically atoroidal 3 orbifold with nonempty ramification locus then o is geometric i e has a metric of constant curvature or is seifert fibred as a corollary any smooth orientationpreserving nonfree finite group action on s3 is conjugate to an orthogonal action

reflexivity and the fixed point property for nonexpansive maps abstract connections between reflexivity and the fixed point property for nonexpansive self mappings of nonempty closed bounded convex subsets of a banach space are investigated in particular it is shown that l 1 for uncountable sets and l cannot even be renormed to have the fixed point property as a consequence if an orlicz space on a finite measure space that is not purely atomic is endowed with the orlicz norm the orlicz space has the fixed point property exactly when it is reflexive

asymptotic behavior of nonoscillatory solutions to n th order nonlinear neutral differential equations abstract for a class of n th order nonlinear neutral differential equations sufficient conditions for all nonoscillatory solutions to satisfy lim t t 1 n x t a are established for another class of equations necessary and sufficient conditions for nonoscillatory solutions to satisfy the above condition are obtained our theorems complement and extend recent results reported in the literature

semiclassical mechanics of the wigner 6j symbol the semiclassical mechanics of the wigner 6j symbol is examined from the standpoint of wkb theory for multidimensional integrable systems to explore the geometrical issues surrounding the ponzano regge formula the relations among the methods of roberts and others for deriving the ponzano regge formula are discussed and a new approach based on the recoupling of four angular momenta is presented a generalization of the yutsis type of spin network is developed for this purpose special attention is devoted to symplectic reduction the reduced phase space of the 6j symbol the 2 sphere of kapovich and millson and the reduction of poisson bracket expressions for semiclassical amplitudes general principles for the semiclassical study of arbitrary spin networks are laid down some of these were used in our recent derivation of the asymptotic formula for the wigner 9j symbol

a characterization of compact convex polyhedra in hyperbolic 3 space in this paper we study the extrinsic geometry of convex polyhedral surfaces in three dimensional hyperbolic spaceh 3 we obtain a number of new uniqueness results and also obtain a characterization of the shapes of convex polyhedra inh 3 in terms of a generalized gauss map this characterization greatly generalizes andre ev s theorem

a sublinear oscillation theorem abstract an oscillation criterion is given for the second order nonlinear differential equation y a t y 0 where a t is continuous but is not assumed to be non negative for all large values of t and y is non decreasing in y and satisfies y y 0 for y 0 this result generalizes a recent extension of belohorec s theorem due to kwong and wong and also incorporates an earlier result of coles

linearization of second order nonlinear oscillation theorems the problem of oscillation of super and sublinear emden fowler equations is studied established are a number of oscillation theorems involving comparison with related linear equations recent results on linear oscillation can thus be used to obtain interesting oscillation criteria for nonlinear equations 25 references

oscillation of solutions of second order nonlinear differential equations of euler type we consider the nonlinear euler differential equation t 2 x g x 0 here g x satisfies xg x 0 for x 0 but is not assumed to be sublinear or superlinear we present implicit necessary and sufficient condition for all nontrivial solutions of this system to be oscillatory or nonoscillatory also we prove that solutions of this system are all oscillatory or all nonoscillatory and cannot be both we derive explicit conditions and improve the results presented in the previous literature we extend our results to the extended

fixed point properties for semigroups of nonlinear mappings and amenability abstract in this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a banach space we also study a schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space such semigroups properly include the class of extremely left amenable semitopological semigroups the free commutative semigroup on one generator and the bicyclic semigroup s 1 a b a b 1

an application of integral inequality to second order nonlinear oscillation abstract a simple result concerning integral inequalities enables us to give an alternative proof of waltman s theorem lim t t 0 a s ds implies oscillation of the second order nonlinear equation y t a t f y t 0 to prove an analog of wintner s theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations assuming that lim t t 0 a s ds exists and to give an alternative proof and to extend a result of butler an often used condition on the coefficient a t is given a more familiar equivalent form and an oscillation criterion involving this condition is established

new families of nonreflexive banach spaces with the fixed point property abstract in this paper we define the concept of sequentially separating norm and we relate it to the fulfillment of the fixed point property for nonexpansive mappings we develop a technique to construct families of nonreflexive banach spaces with the fixed point property different examples will be exhibited we also study the geometry of the banach spaces that can be renormed with a sequentially separating norm

rigidity of infinite disk patterns let p be a locally flnite disk pattern on the complex plane c whose combinatorics are described by the one skeleton g of a triangulation of the open topological disk and whose dihedral angles are equal to a function e 0 2 on the set of edges let p be a combinatorially equivalent disk pattern on the plane with the same dihedral angle function we show that p and p difier only by a euclidean similarity in particular when the dihedral angle function is identically zero this yields the rigidity theorems of b rodin and d sullivan and of o schramm whose arguments rely essentially on the pairwise disjointness of the interiors of the disks the approach here is analytical and uses the maximum principle the concept of vertex extremal length and the recurrency of a family of electrical networks obtained by placing resistors on the edges in the contact graph of the pattern a similar rigidity property holds for locally flnite disk patterns in the hyperbolic plane where the proof follows by a simple use of the maximum principle also we have a uniformization result for disk patterns in a future paper the techniques of this paper will be extended to the case when 0 in particular we will show a rigidity property for a class of inflnite convex polyhedra in the 3 dimensional hyperbolic space

on the structure of the set of equivalent norms on l1 with the fixed point property abstract let a be the set of all equivalent norms on l 1 which satisfy the fpp we prove that a contains rays in fact every renorming in l 1 which verifies condition in theorem 2 1 is the starting point of a closed or open ray composed by equivalent norms on l 1 with the fpp the standard norm 1 or p k lin s norm defined in lin 2008 12 are examples of such norms moreover we study some topological properties of the set a with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to 1

voronoi diagrams on piecewise flat surfaces and an application to biological growth this paper introduces the notion of voronoi diagrams and delaunay triangulations generated by the vertices of a piecewise flat triangulated surface based on properties of such structures a generalized flip algorithm to construct the delaunay triangulation and voronoi diagram is presented an application to biological membrane growth modeling is then given a voronoi partition of the membrane into cells is maintained during the growth process which is driven by the creation of new cells and by restitutive forces of the elastic membrane

existence and nonoscillation theorems for an emden fowler equation with deviating argument on donne des conditions suffisantes pour qu une equation d emden fowler generalisee a argument devie possede des solutions non oscillatoires a comportement asymptotique prescrit pour t

isolated singularities of the solutions of the schrodinger equation with a radial potential we study the behavior near an isolated singularity say x 0 of solutions of the equation 1 u x v x u x defined in a neighborhood of 0 in terms of the potential v which we assume to be radially symmetric for a class of potentials p1 that we characterize completely there is a unique singularity with constant sign behaving like the fundamental solution of the laplace operator for a larger class p2 we obtain a unique type of nonnegative singularity that is radially symmetric if v r cr with c 0 e r the class p1 is characterized by 2 and the class p2 by 2 the results fail for 2

oscillation of solutions of second order nonlinear self adjoint differential equations abstract we are concerned with the oscillation problem for the nonlinear self adjoint differential equation a t x b t g x 0 here g x satisfied the signum condition xg x 0 if x 0 but is not imposed such monotonicity as superlinear or sublinear we show that certain growth conditions on g x play an essential role in a decision whether all nontrivial solutions are oscillatory or not our main theorems extend recent results in a serious of papers and are best possible for the oscillation of solutions in a sense to accomplish our results we use sturm s comparison method and phase plane analysis of systems of lienard type we also explain an analogy between our results and an oscillation criterion of kneser hille type for linear differential equations

characterizations of circle patterns and finite convex polyhedra in hyperbolic 3 space the aim of this paper is to study finite convex polyhedra in three dimensional hyperbolic space mathbb h 3 we characterize the quasiconformal deformation space of each finite convex polyhedron as a corollary we obtain some results on finite circle patterns in the riemann sphere with dihedral angle 0 le theta pi that is for any circle pattern on hat mathbb c its quasiconformal deformation space can be naturally identified with the product of the teichmuller spaces of its interstices

small deformations of polygons and polyhedra we describe the first order variations of the angles of euclidean spherical or hyperbolic polygons under infinitesimal deformations such that the lengths of the edges do not change using this description we introduce a vector valued quadratic invariant b on the space of those isometric deformations which for convex polygons has a remarkable positivity property we give two geometric applications the first is an isoperimetric statement for hyperbolic polygons among the convex hyperbolic polygons with given edge lengths there is a unique polygon with vertices on a circle a horocycle or on one connected component of the space of points at constant distance from a geodesic and it has maximal area the second application is a rigidity result for equivariant polyhedral surfaces in the minkowski space on decrit les deformations infinitesimales des angles d un polygone euclidien spherique ou hyperbolique sous les deformations infinitesimales qui preservent les longueurs des aretes on en deduit la definition d un invariant quadratique a valeurs vectorielles b sur l espace de ces deformations isometriques qui pour les polygones convexes a une propriete remarquable de positivite on donne deux applications geometriques la premiere est un enonce isoperimetrique pour les polygones hyperboliques parmi les polygones hyperboliques convexes dont les longueurs des aretes sont donnees il existe un unique element dont les sommets sont sur un cercle un horocycle ou dans une composante connexe de l ensemble des points a distance constante d une geodesique et son aire est maximale la seconde application est un resultat de rigidite pour les surfaces polyedrales equivariantes dans l espace de minkowski

asymptotic behavior of solutions of second order quasilinear differential equations with delay depending on the unknown function the asymptotic behavior of the nonoscillatory solutions of quasilinear differential equations of second order with delay depending on the unknown function is considered the main results given by bainov et al j comput appl math 91 1998 87 96 and wong funkcial ekvac 11 1968 207 234 are improved and generalized

integral inequalities of gronwall bellman bihari type and asymptotic behavior of certain second order nonlinear differential equations abstract several integral inequalities similar to gronwall bellmann bihari inequalities are obtained these inequalities are used to discuss the asymptotic behavior of certain second order nonlinear differential equations

distortion and stability of the fixed point property for non expansive mappings abstract let x be a banach space we say that x satisfies the fixed point property weak fixed point property if every non expansive mapping defined from a convex closed bounded convex weakly compact subset of x into itself has a fixed point we say that x satisfies the stable fixed point property stable weak fixed point property if the same is true for every equivalent norm which is close enough to the original one denote by p x the set formed by all equivalent norms with the topology of the uniform convergence on the unit ball of x we prove that the subset of p x formed by the norms failing the fixed point property is dense in p x when x is a non distortable space which fails the fixed point property in particular no renorming of l 1 can satisfy the stable fixed point property furthermore we show some examples of distortable spaces failing the weak fixed point property which can be renormed to satisfy the stable weak fixed point property as a consequence we prove that every separable banach space can be renormed to satisfy the stable weak fixed point property

on the asymptotic integration of nonlinear differential equations the aim of the present paper is twofold firstly the paper surveys the literature concerning a specific topic in asymptotic integration theory of ordinary differential equations the class of second order equations with bihari like nonlinearity secondly some general existence results are established with regard to a condition that has been found recently to be of significant use in the theory of elliptic partial differential equations

fuchsian polyhedra in lorentzian space forms let s be a compact surface of genus 1 and g be a metric on s of constant curvature k in 1 0 1 with conical singularities of negative singular curvature when k 1 we add the condition that the lengths of the contractible geodesics are 2 we prove that there exists a convex polyhedral surface p in the lorentzian space form of curvature k and a group g of isometries of this space such that the induced metric on the quotient p g is isometric to s g moreover the pair p g is unique up to global isometries among a particular class of convex polyhedra namely fuchsian polyhedra this extends theorems of alexandrov and rivin hodgson rec math mat sbornik ns 11 53 15 65 1942 invent math 111 1 77 111 1993 concerning the sphere to the higher genus cases and it is also the polyhedral version of a theorem of labourie and schlenker math ann 316 3 465 483 2000

existence and multiplicity of solutions for nonlinear second order difference boundary value problems in the present paper the following nonlinear second order difference boundary value problems d p n 1 du n 1 q n u n f n u n 0 n z 1 n u 0 u n p 0 du 0 p n du n are studied by using the critical theory and three new multiple results of solutions are obtained where z 1 n 1 2 n f z 1 n xr r is a continuous function in the second variable p q z 0 n r and p n 0

embeddings of non positively curved compact surfaces in flat lorentzian manifolds we prove that any metric of non positive curvature in the sense of alexandrov on a compact surface can be isometrically embedded as a convex spacelike cauchy surface in a flat spacetime of dimension 2 1 the proof follows from polyhedral approximation

asymptotic integration of nonlinear ϕ laplacian differential equations abstract the aim of the present paper is to study the existence of solutions to initial values problems for a laplace like operator we generalize the results of agarwal 2007 1 section 4 theorem 3 and the result of philos 2004 20 theorem 5 to the laplacian like problems

on the stability of the positive radial steady states for a semilinear cauchy problem abstract this paper is a contribution to the analysis of the cauchy problem 0 1 u t u i 1 k c i x l i u p i in r n 0 t u x 0 x in r n with initial function 0 the stability and asymptotic stability of the positive radial steady states which are positive solutions of 0 2 u i 1 k c i x l i u p i 0 have been discussed with in weighted banach spaces

global existence of solutions with prescribed asymptotic behavior for second order nonlinear differential equations where the nonlinearity f satis9es certain monotonicity conditions speci9ed in the sequel we always assume without mentioning that the function f t u v is continuous in the domain d t u v t t0 u v r where t0 1 it is supposed also that all equations and inequalities involving t hold for t t0 unless otherwise speci9ed the symbols o and o have their standard meanings as t and we use the notation r def 0 eq 1 is often used for mathematical modelling of various physical chemical and biological systems and attracts constant interest of researchers a great deal of papers published during the last three decades are concerned with local and global existence of solutions of eq 1 and its numerous particular cases uniqueness of solutions

renormings failing to have asymptotically isometric copies of l1 or c0 abstract it is proved that every equivalent norm in l 1 is the starting point of a ray of norms which fail to have an asymptotically isometric copy of l 1 in the case where x is separable it is proved that the set of all equivalent norms in x which fail to have an asymptotically isometric copy of l 1 is residual similar results are obtained for the case of c 0 in particular we deduce that every separable banach space has an equivalent norm for which it fails to contain an asymptotically isometric copy of l 1 and c 0

prescribing curvature on compact surfaces with conical singularities we study the berger nirenberg problem on surfaces with conical singularities i e we discuss conditions under which a function on a riemann surface is the gaussian curvature of some conformal metric with a prescribed set of singularities of conical types

surfaces convexes fuchsiennes dans les espaces lorentziens a courbure constante we show existence and uniqueness of the equivariant isometric immersions of riemannian surfaces into lorentz space forms under conditions implying convexity when we impose that the associated representations leave a point invariant