global solutions for a semilinear two dimensional klein gordon equation with exponential type nonlinearity we prove the existence and uniqueness of global solutions for a cauchy problem associated to a semilinear klein gordon equation in two space dimensions our result is based on an interpolation estimate with a sharp constant obtained by a standard variational method 2006 wiley periodicals inc

stable subharmonic solutions in periodic reaction diffusion equations we construct an example of a t periodic semilinear reaction diffusion equation whose elliptic part is in divergence form for each t and which admits stable periodic solutions of higher minimal period thus there is no generic convergence to t periodic solutions this is in sharp contrast to the autonomous case where the existence of a lyapunov function implies quasiconvergence for all bounded solutions

determinants of laplacians the determinant of the laplacian on spinor fields on a riemann surface is evaluated in terms of the value of the selberg zeta function at the middle of the critical strip a key role in deriving this relation is played by the barnes double gamma function

eta invariants and regularized determinants for odd dimensional hyperbolic manifolds with cusps we study eta invariants of dirac operators and regularized determinants of dirac lapla cians over hyperbolic manifolds with cusps and their relations with selberg zeta functions using the selberg trace formula and a detailed analysis of the unipotent orbital integral we show that the eta and zeta functions defined by the relative traces are regular at the origin so that we can define the eta invariant and the regularized determinant we also show that the selberg zeta function of odd type has a meromorphic extension over c prove a relation of the eta invariant and a certain value of the selberg zeta function of odd type and derive a corresponding functional equation these results generalize the earlier work of john millson to hyperbolic manifolds with cusps we also prove that the selberg zeta function of even type has a meromorphic extension over c relate it to the regularized determinant and obtain a corresponding functional equation

instability for standing waves of nonlinear klein gordon equations via mountain pass arguments we introduce mountain pass type arguments in the context of orbital instability for klein gordon equations our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital stability instability for a power type nonlin earity we prove that the ground states of the associated stationary equation are minimizers of the functional action on a wide variety of constraints for a general nonlinearity we extend to the dimension n 2 the classical in stability result for stationary solutions of nonlinear klein gordon equations proved in 1985 by shatah in dimension n 3

the selberg trace formula and selberg zeta function for cofinite kleinian groups with finite dimensional unitary representations for cofinite kleinian groups with finite dimensional unitary representations we derive the selberg trace formula as an application we define the corresponding selberg zeta function and compute its divisor thus generalizing results of elstrodt grunewald and mennicke to non trivial unitary representations we show that the presence of cuspidal elliptic elements sometimes adds ramification points to the zeta function in fact if open image in new window is the ring of eisenstein integers then the selberg zeta function of open image in new window contains ramification points and is the sixth root of a meromorphic function

scattering for a critical nonlinear wave equation in two space dimensions we show that the solutions to the cauchy problem for a wave equation with critical exponential nonlinearity in 2 space dimensions scatter for arbitrary smooth compactly supported initial data

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

structural stability for time periodic one dimensional parabolic equations denote q w x 0 l x r the nonlinear term f is assumed to satisfy the following conditions f l f q r is of class c f 2 f t l x u f t x u for all te w xe o l and uer define a self adjoint operator a in x l2 0 l by a t bxx for e d a h2 0 l a ha o l for each c1 e r let a be the fractional power of a and x d a be the fractional power space equipped with the graph norm ii 11 xn 1111 11x iia i ii x throughout this section we fix a c1 1 by the above assumptions f l f 2 for any u0 e x there exists a unique local in time classical solution u t x u t x of

symmetric and arbitrarily high order birkhoff hermite time integrators and their long time behaviour for solving nonlinear klein gordon equations abstract the klein gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering its computation represents a major challenge the main theme of this paper is the construction of symmetric and arbitrarily high order time integrators for the nonlinear klein gordon equation by integrating birkhoff hermite interpolation polynomials to this end under the assumption of periodic boundary conditions we begin with the formulation of the nonlinear klein gordon equation as an abstract second order ordinary differential equation ode and its operator variation of constants formula we then derive a symmetric and arbitrarily high order birkhoff hermite time integration formula for the nonlinear abstract ode accordingly the stability convergence and long time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi definite matrix subject to suitable temporal and spatial smoothness a remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for pdes in the literature numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches

scattering theory in the energy space for a class of non linear wave equations we study the asymptotic behaviour in time of the solutions and the theory of scattering in the energy space for the non linear wave equation square varphi f varphi 0 in n n 3 we prove the existence of the wave operators asymptotic completeness for small initial data and forn 4 asymptotic completeness for arbitrarily large data the assumptions onf cover the case wheref behaves slightly better than a single powerp 1 4 n 2 both near zero and at infinity see 1 5 1 6 and 1 8

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

almost periodically forced circle flows abstract we study general dynamical and topological behaviors of minimal sets in skew product circle flows in both continuous and discrete settings with particular attentions paying to almost periodically forced circle flows when a circle flow is either discrete in time and unforced i e a circle map or continuous in time but periodically forced behaviors of minimal sets are completely characterized by classical theory the general case involving almost periodic forcing is much more complicated due to the presence of multiple forcing frequencies the topological complexity of the forcing space and the possible loss of mean motion property on one hand we will show that to some extent behaviors of minimal sets in an almost periodically forced circle flow resemble those of denjoy sets of circle maps in the sense that they can be almost automorphic cantorian and everywhere non locally connected but on the other hand we will show that almost periodic forcing can lead to significant topological and dynamical complexities on minimal sets which exceed the contents of denjoy theory for instance an almost periodically forced circle flow can be positively transitive and its minimal sets can be li yorke chaotic and non almost automorphic as an application of our results we will give a complete classification of minimal sets for the projective bundle flow of an almost periodic sl 2 r valued continuous or discrete cocycle continuous almost periodically forced circle flows are among the simplest non monotone multi frequency dynamical systems they can be generated from almost periodically forced nonlinear oscillators through integral manifolds reduction in the damped cases and through mather theory in the damping free cases they also naturally arise in 2d almost periodic floquet theory as well as in climate models discrete almost periodically forced circle flows arise in the discretization of nonlinear oscillators and discrete counterparts of linear schrodinger equations with almost periodic potentials they have been widely used as models for studying strange non chaotic attractors and intermittency phenomena during the transition from order to chaos hence the study of these flows is of fundamental importance to the understanding of multi frequency driven dynamical irregularities and complexities in non monotone dynamical systems

on minimal sets of scalar parabolic equations with skew product structures skew product semi flow i t x x y x x y which is generated by ut uxx f y t ix u ux t 0 0 x 1 y e y d or n boundary conditions is considered where x is an appropriate subspace of h2 0 1 y r is a minimal flow with compact phase space it is shown that a minimal set e c x x y of ilt is an almost 1 1 extension of y that is set yo y e y i card e c p 1 y i is a residual subset of y where p x x yy is the natural projection consequently if y r is almost periodic minimal then any minimal set e c x x y of ilt is an almost automorphic minimal set it is also proved that dynamics of it is closed in the category of almost automorphy that is a minimal set e c x x y of fit is almost automorphic minimal if and only if y r is almost automorphic minimal asymptotically almost periodic parabolic equations and certain coupled parabolic systems are discussed examples of nonalmost periodic almost automorphic minimal sets are provided

brezis gallouet wainger type inequality with a double logarithmic term in the holder space its sharp constants and extremal functions we investigate the sharp constants in a brezis gallouet wainger type inequality with a double logarithmic term in the holder space in a bounded domain in r n ibrahim majdoub and masmoudi gave the sharp constant in the 2 dimensional case we make precise estimates to give the sharp constants and pass to the case of higher dimensions n 2 we can also show that the inequality with fixed constants including the sharp ones admits an extremal function under a suitable condition when the domain is a ball 2000 mathematics subject classification primary 46e35 secondary 35j85

a poincare bendixson theorem for scalar reaction diffusion equations for scalar equations u t u xx f x u u x with x e s 1 and f e c 2 we show that the classical theorem of poincare and bendixson holds the limit set of any bounded solution satisfies exactly one of the following alternatives this is surprising because the system is genuinely infinite dimensional

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

equivalent moser type inequalities in r2 and the zero mass case abstract we first investigate concentration and vanishing phenomena concerning moser type inequalities in the whole plane which involve complete and reduced sobolev norms in particular we show that the critical ruf inequality is equivalent to an improved version of the subcritical adachi tanaka inequality which we prove to be attained then we consider smooth compactly supported functions with respect to the dirichlet norm 2 and we prove an optimal lorentz zygmund type inequality with explicit extremals and from which can be derived classical inequalities in h 1 r 2 such as the adachi tanaka inequality and a version of ruf s inequality

almost periodic dynamics of perturbed infinite dimensional dynamical systems abstract this paper is concerned with the dynamics of an infinite dimensional gradient system under small almost periodic perturbations under the assumption that the original autonomous system has a global attractor given as the union of unstable manifolds of a finite number of hyperbolic equilibrium solutions we prove that the perturbed non autonomous system has exactly the same number of almost periodic solutions as a consequence the pullback attractor of the perturbed system is given by the union of unstable manifolds of these finitely many almost periodic solutions an application of the result to the chafee infante equation is discussed

almost periodic attractors for a class of nonautonomous reaction diffusion equations on rn i global stabilization processes in this paper we investigate global stabilization phenomena of certain classical solutions to nonautonomous semilinear parabolic partial differential equations with neumann boundary conditions on bounded domains in rn given any such classical solution u we prove in particular that there exists a spatially homogeneous time almost periodic classical solution u which captures u with respect to an appropriate sobolev norm as the time variable goes to infinity the class of equations which we analyze here contains in particular fisher s type reaction diffusion equations of population genetics our method of investigation mainly rests upon a combination of some geometric arguments with parabolic comparison principles

transversality of homoclinic orbits and exponential dichotomies for parabolic equations abstract in this paper we discuss the existence of exponential dichotomies on r of linear parabolic equations depending on small parameters and provide a tool of proving the transversality of the homoclinic orbits of parabolic equations and by making use of the results on exponential dichotomies of this paper we investigate the transversality of homoclinic orbits for parabolic equations

asymptotic expansions and extremals for the critical sobolev and gagliardo nirenberg inequalities on a torus we give a comprehensive study of interpolation inequalities for periodic functions with zero mean including the existence of and the asymptotic expansions for the extremals best constants various remainder terms etc most attention is paid to the critical logarithmic sobolev inequality in the two dimensional case although a number of results concerning the best constants in the algebraic case and different space dimensions are also obtained

almost automorphic solutions for stochastic differential equations driven by levy noise abstract we introduce the concepts of poisson square mean almost automorphy and almost automorphy in distribution under suitable conditions on the coefficients we establish the existence of solutions which are almost automorphic in distribution for some semilinear stochastic differential equations with infinite dimensional levy noise we further discuss the global asymptotic stability of these solutions finally to illustrate the theoretical results obtained in this paper we give several examples

regular articlegeneralized strichartz inequalities for the wave equation we make a synthetic exposition of the generalized strichartz inequalities for the wave equation obtained in 6 together with the limiting cases recently obtained in 13 with as simple proofs as possible the proofs combine stationary phase estimates dyadic decompositions the hardy littlewood inequality or the holder inequality in time and abstract duality and interpolation arguments

explicit estimates on the torus for the sup norm and the dissipative length scale of solutions of the swift hohenberg equation in one and two space dimensions abstract in this work we have obtained explicit and accurate estimates of the sup norm for solutions of the swift hohenberg equation she in one and two space dimensions by using the best so far available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations we have evaluated in an explicit manner the values of the sup norm of the solutions of the she in addition we have calculated the so called time averaged dissipative length scale associated to the above solutions

strichartz type estimates and the well posedness of an energy critical 2d wave equation in a bounded domain abstract we study the well posedness of the cauchy problem with dirichlet or neumann boundary conditions associated to an h 1 critical semilinear wave equation on a smooth bounded domain r 2 first we prove an appropriate strichartz type estimate using the l q spectral projector estimates of the laplace operator our proof follows burq lebeau and planchon 2008 4 then we show the global well posedness when the energy is below or at the threshold given by the sharp moser trudinger inequality finally in the supercritical case we prove an instability result using the finite speed of propagation and a quantitative study of the associated ode with oscillatory data

evolution semigroups translation algebras and exponential dichotomy of cocycles abstract we study the exponential dichotomy of an exponentially bounded strongly continuous cocycle over a continuous flow on a locally compact metric space acting on a banach space x our main tool is the associated evolution semigroup on c 0 x we prove that the cocycle has exponential dichotomy if and only if the evolution semigroup is hyperbolic if and only if the imaginary axis is contained in the resolvent set of the generator of the evolution semigroup to show the latter equivalence we establish the spectral mapping annular hull theorem for the evolution semigroup in addition dichotomy is characterized in terms of the hyperbolicity of a family of weighted shift operators defined on c 0 z x here we develop banach algebra techniques and study weighted translation algebras that contain the evolution operators these results imply that dichotomy persists under small perturbations of the cocycle and of the underlying compact metric space also exponential dichotomy follows from pointwise discrete dichotomies with uniform constants finally we extend to our situation the classical perron theorem which says that dichotomy is equivalent to the existence and uniqueness of bounded continuous mild solutions to the inhomogeneous equation

dynamics in coupled oscillators with recurrent random forcing a pde approach the current paper is devoted to the study of coupled oscillators with recurrent random forcing special attention is given to the solutions having the same recurrence randomness as that of the forcing recurrent random solutions for short by embedding coupled oscillators into coupled parabolic equations it establishes a general theorem on the existence of recurrent random solutions it also finds conditions under which such solutions are unique when the recurrent forcing is actually quasi periodic or almost periodic recurrent solutions are refereed to as quasi periodic or almost periodic solutions in a weak sense and they are quasi periodic or almost periodic in the classical sense under the uniqueness conditions in addition applications of the general theory to coupled duffing type oscillators and josephson junctions are considered and the results obtained extend several existing ones for quasi periodic duffing oscillators

sharp constants in the sobolev embedding theorem and a derivation of the brezis gallouet interpolation inequality sharp estimates are obtained for the constants appearing in the sobolev embedding theorem on the two dimensional torus furthermore a version of the brezis gallouet interpolation inequality is obtained with an explicit but not necessarily optimal constant in the leading term namely the logarithmic term the constants are expressed in terms of the riemann zeta function and the dirichlet beta series

the global cauchy problem for the critical non linear wave equation abstract we study the global cauchy problem for the non linear wave equation p 1 0 for the critical value p n 2 n 2 in space dimension n 3 we identify a weak space time integrability property stip of the solutions and prove that it is sufficient to ensure the uniqueness of weak solutions the global existence of finite energy solutions with the naturally associated stip and the global existence of regular solutions with some n dependent restrictions on the regularity for spherically symmetric solutions we prove that the previous crucial stip follows from the morawetz inequality actually in a much stronger form than necessary thereby proving that all the previous results hold in the spherically symmetric case

oscillations and concentration effects in semilinear dispersive wave equations let un be a sequence of smooth solutions to a dispersive nonlinear wave equation formula inr1 3 with uniformly compactly supported cauchy data converging weakly to 0 inh1 r3 l2 r3 let vn be the sequence of solutions to the linear wave equation with the same cauchy data we show thatun vngoes strongly to 0 in the energy spacec 0 t h1 c1 0 t l2 if f is a subcritical nonlinearity in the critical casef u u5 we show that this property is equivalent tovn 0 inl 0 t l6 then we give sharp sufficient conditions on microlocal measures associated to the data the proof relies on a microlocal version of p l lions concentration compacity soit un une suite de solutions regulieres d une equation d ondes non lineaire dispersive formula dansr1 3 avec donnees de cauchy supportees dans un compact fixe et convergeant faiblement vers 0 dansh1 r3 l2 r3 soit vn la suite des solutions de l equation des ondes lineare avec les memes donnees de cauchy on montre queun vnconverge fortement vers 0 dans l espace d energiec 0 t h1 c1 0 t l2 sifest une non linearite sous critique dans le cas critiquef u u5 on montre que cette propriete equivaut a la convergence forte devnvers 0 dansl 0 t l6 on en donne alors des conditions suffisantes optimales en termes de mesures microlocales associees aux donnees la demonstration est basee sur une version microlocale de la concentration compacite de p l lions

determinants of laplacians and isopolar metrics on surfaces of infinite area we construct a determinant of the laplacian for infinite area surfaces which are hyperbolic near infinity and without cusps in the case of a convex co compact hyperbolic metric the determinant can be related to the selberg zeta function and thus shown to be an entire function of order two with zeros at the eigenvalues and resonances of the laplacian in the hyperbolic near infinity case the determinant is analyzed through the zeta regularized relative determinant for a conformal metric perturbation we establish that this relative determinant is a ratio of entire functions of order two with divisor corresponding to eigenvalues and resonances of the perturbed and unperturbed metrics these results are applied to the problem of compactness in the smooth topology for the class of metrics with a given set of eigenvalues and resonances

regularized determinants of the laplacian for cofinite kleinian groups with finite dimensional unitary representations for cofinite kleinian groups or equivalently finite volume three dimensional hyperbolic orbifolds with finite dimensional unitary representations we evaluate the regularized determinant of the laplacian using w muller s regularization we give an explicit formula relating the determinant to the selberg zeta function

convergence asymptotic periodicity and finite point blow up in one dimensional semilinear heat equations abstract we consider the initial value problem for the semilinear heat equation u t u xx f u t 0 x l t 0 under the dirichlet the neumann or the periodic boundary conditions we show that each solution whether it exists globally for t 0 or blows up in a finite time possesses an asymptotic profile in a certain sense and tends to this profile as time increases in the special case where f u t t f u t for some t 0 among other things the above statement is interpreted as saying that any bounded global solution converges as t to a time t periodic solution having some specific spatial structure in the case where the solution blows up in a finite time say at t t 0 assuming simply that f is a smooth function satisfying some growth conditions and that the initial data is a nonconstant bounded function we prove that the blow up set is a finite set and that lim t t 0 u x t x exists with being a smooth function having at most finitely many singular points

high frequency approximation of solutions to critical nonlinear wave equations this work is devoted to the description of bounded energy sequences of solutions to the equation 1 u u 4 0 in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i up to remainder terms small in energy norm and in every strichartz norm the proof relies on scattering theory for 1 and on a structure theorem for bounded energy sequences of solutions to the linear wave equation in particular we infer the existence of an a priori estimate of strichartz norms of solutions to 1 in terms of their energy

determinants of laplacians on surfaces of finite volume determinants of the laplace and other elliptic operators on compact manifolds have been an object of study for many years see mp rs vor up until now however the theory of determinants has not been extended to non compact situations since these typically involve a mixture of discrete and continuous spectra recent advances in this theory which are partially motivated by developments in mathematical physics have led to a connection in the compact riemann surface case between determinants of laplacians on spinors and the selberg zeta function of the underlying surface see dp kie sar vor

the dynamics of rotating waves in scalar reaction diffusion equations on etudie l attracteur compact maximal pour l equation u t u xx f u u x avec des conditions aux limites periodiques on montre qu un ensemble limite contient une onde de rotation

the zero set of a solution of a parabolic equation on etudie l ensemble nul d une solution u t x de l equation u t a x t u xx b x t u x c x t u sous des hypotheses tres generales sur les coefficients a b et c

complicated dynamics in scalar semilinear parabolic equations in higher space dimension abstract we study the dynamics of the boundary value problem ut lu g x u u x 1 u 0 2 where l is a second order uniformly elliptic operator and r n is diffeomorphic to the ball in r n n 2 the main result asserts that given any ck vector field v on r n 1 with v 0 0 one can adjust coefficients of l and the function g such that the corresponding problem 1 2 has an n 1 dimensional invariant manifold through the equilibrium u 0 and the taylor expansion at u 0 of the vector field representing the flow on this manifold coincides in appropriate coordinates with the taylor expansion of v up to k th order terms this result implies that a hyperbolic invariant n torus can be found in 1 2 if l and g are appropriately chosen this result also indicates that chaotic dynamics is likely to occur for some choices of l and g

asymptotic behavior of the selberg zeta functions for degenerating families of hyperbolic manifolds let mk be a degenerating sequence of finite volume hyperbolic manifolds of dimension d with d 2 or d 3 with finite volume limit m let z m k s be the associated sequence of selberg zeta functions and let mathcal z k s be the product of local factors in the euler product expansion of z m k s corresponding to the pinching geodesics on mk the main result in this article is to prove that z m k s mathcal z k s converges to z m infty s for all s in mathbf c with re s d 1 2 the significant feature of our analysis is that the convergence of z m k s mathcal z k s to z m infty s is obtained up to the critical line including the right half of the critical strip a region where the euler product definition of the selberg zeta function does not converge in the case d 2 our result reproves by different means the main theorem in schulze j funct anal 236 120 160 2006

determinant of the laplacian on a non compact three dimensional hyperbolic manifold with finite volume the functional determinant of laplace type operators on a three dimensional non compact hyperbolic manifold with invariant fundamental domain of finite volume is expressed via the selberg zeta function related to the picard group

floquet bundles for scalar parabolic equations for linear scalar parabolic equations such as u t u xx a t x u x b t x u on a finite interval 0 x with various boundary conditions we obtain canonical floquet solutions u n t x these solutions are characterized by the property that z u n t x n for all te where z denotes the zero crossing lap number of matano the coefficients a t x and b t x are not assumed to be periodic in t but if they are the solutions u n t x reduce to the standard floquet solutions our results may naturally be expressed in the language of linear skew product flows in this context we obtain for each n 1 an exponential dichotomy between the bundles span u n 1 and overline span u n cdot cdot n n 1 infty

discretized characterizations of exponential dichotomy of linear skew product semiflows over semiflows using the method of discretization we investigate the necessary and sufficient conditions for the existence of exponential dichotomy of linear skew product semiflows over semiflows through the existence of discrete exponential dichotomy of the discretized linear skew product semiflows we then apply the obtained results to consider the roughness of exponential dichotomy of linear skew product semiflows

relative zeta functions relative determinants and scattering theory we use the method of zeta function regularization to regularize the ratio det a det a0 of the determinants of two elliptic self adjoint operators a a0 satisfying certain natural assumptions this is of interest especially if the regularized determinants of the individual operators don t exist as for example in the case of elliptic operators on a noncompact manifold

a blowing up wave equation with exponential type nonlinearity and arbitrary positive energy abstract we consider in two space dimensions the nonexistence of global solutions to the class of klein gordon equations t t u u u f a u t x 0 t we give sufficient conditions on the data such that the solution of the above klein gordon equation blows up in finite time

on the growth of l 2 invariants for sequences of lattices in lie groups we study the asymptotic behaviour of betti numbers twisted torsion and other spectral invariants of sequences of locally symmetric spaces our main results are uniform versions of the degeorge wallach theorem of a theorem of delorme and various other limit multiplicity theorems a basic idea is to adapt the notion of benjamini schramm convergence bs convergence originally introduced for sequences of finite graphs of bounded degree to sequences of riemannian manifolds and analyze the possible limits we show that bs convergence of locally symmetric spaces g k implies convergence in an appropriate sense of the normalized relative plancherel measures associated to l2 g this then yields convergence of normalized multiplicities of unitary representations betti numbers and other spectral invariants on the other hand when the corresponding lie group g is simple and of real rank at least two we prove that there is only one possible bs limit i e when the volume tends to infinity locally symmetric spaces always bs converge to their universal cover g k this leads to various general uniform results when restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of bs convergence which in turn implies upper estimates on the rate of convergence of normalized betti numbers in the spirit of sarnak xue an important role in our approach is played by the notion of invariant random subgroups for higher rank simple lie groups g we exploit rigidity theory and in particular the nevo stuck zimmer theorem and kazhdan s property t to obtain a complete understanding of the space of irs s of g 2017 department of mathematics princeton university

convergence in smooth strongly monotone flows defined by semilinear parabolic equations on considere des equations paraboliques semi lineaires dy dt ay f y ou a est un operateur sectoriel sur un banach x ayant une resolvante compacte et f est une c 2 application de l espace des puissances fractionnaires x 0 1 dans x soit y t une solution qui est quasi convergente mais non convergente alors il existe un voisinage u de y 0 y 0 avec la propriete suivante si z u y 0 a une trajectoire bornee et soit z y 0 soit z y 0 alors la solution partant de z converge vers un equilibre

on determinants of laplacians on riemann surfaces determinants of laplacians on tensors and spinors of arbitrary weights on compact hyperbolic riemann surfaces are computed in terms of values of selberg zeta functions at half integer points