the poisson embedding approach to the calderon problem we introduce a new approach to the anisotropic calderon problem based on a map called poisson embedding that identifies the points of a riemannian manifold with distributions on its boundary we give a new uniqueness result for a large class of calderon type inverse problems for quasilinear equations in the real analytic case the approach also leads to a new proof of the result of lassas et al annales de l ens 34 5 771 787 2001 solving the calderon problem on real analytic riemannian manifolds the proof uses the poisson embedding to determine the harmonic functions in the manifold up to a harmonic morphism the method also involves various runge approximation results for linear elliptic equations

an inverse problem for a semi linear elliptic equation in riemannian geometries abstract we study the inverse problem of unique recovery of a complex valued scalar function v m c c defined over a smooth compact riemannian manifold m g with smooth boundary given the dirichlet to neumann map in a suitable sense for the elliptic semi linear equation g u v x u 0 we show that uniqueness holds for a large class of non linearities when the manifold is conformally transversally anisotropic the proof is constructive and is based on a multiple fold linearization of the semi linear equation near complex geometric optic solutions for the linearized operator and the resulting non linear interactions these interactions result in the study of a weighted integral transform along geodesics that we call the jacobi weighted ray transform

stability in the determination of a time dependent coefficient for wave equations from partial data let be a c2 bounded domain of rn n 2 and fix q 0 t with t 0 we consider the stability in the inverse problem of determining a time dependent coefficient of order zero q appearing in a dirichlet initial boundary value problem for a wave equation t2u xu q t x u 0 in q from partial observations on q the observation is given by a boundary operator associated to the wave equation using suitable geometric optics solutions and carleman estimates we prove a stability estimate in the determination of q from the boundary operator

stable determination of a semilinear term in a parabolic equation in 5 the flrst and third authors establish holder type stability estimates for the inverse problem consisting in the determination of a semilinear term of a parabolic equation from a single boundary measurement when the domain is a rectangle in the present paper we extend the results in 5 for a general smooth domain

completeness of products of solutions and some inverse problems for pde abstract in this paper we give conditions which guarantee that products of solutions of partial differential equations pu au 0 are complete in l 2 here p is a linear partial differential operator with constant coefficients and a is a function in l we check these conditions for elliptic parabolic and hyperbolic equations of second order and give applications to inverse problems for related equations where a is to be found

inverse problems for lorentzian manifolds and non linear hyperbolic equations we study two inverse problems on a globally hyperbolic lorentzian manifold m g the problems are 1 passive observations in spacetime consider observations in an open set v subset m the light observation set corresponding to a point source at q in m is the intersection of v and the light cone emanating from the point q let w subset m be an unknown open relatively compact set we show that under natural causality conditions the family of light observation sets corresponding to point sources at points q in w determine uniquely the conformal type of w 2 active measurements in spacetime we develop a new method for inverse problems for non linear hyperbolic equations that utilizes the non linearity as a tool this enables us to solve inverse problems for non linear equations for which the corresponding problems for linear equations are still unsolved to illustrate this method we solve an inverse problem for semilinear wave equations with quadratic non linearities we assume that we are given the neighborhood v of the time like path mu and the source to solution operator that maps the source supported on v to the restriction of the solution of the wave equation to v when m is 4 dimensional we show that these data determine the topological differentiable and conformal structures of the spacetime in the maximal set where waves can propagate from mu and return back to mu

the euler characteristic of the moduli space of curves let fg 1 g 1 be the mapping class group consisting of all isotopy classes of base point and orientation preserving homeomorphisms of a closed oriented surface f of genus g let 1 be its euler characteristic in the sense of wall that is z f i fgl f l z e f where f is any torsion free subgroup of finite index in f 1 and e is a contractible space on which f acts freely and properly discontinuously an example of such a space is the teichmiiller space 1 and g f can be interpreted as the orbifold euler characteristic of f i join the moduli space of curves of genus g with base point the purpose of this paper is to prove the following formula for f i

determination of viscosity in the stationary navier stokes equations abstract in this paper we consider the stationary navier stokes equations in a bounded domain with a variable viscosity we prove that one can uniquely determine the viscosity function from the knowledge of boundary data

a discrete uniformization theorem for polyhedral surfaces a notion of discrete conformality for hyperbolic polyhedral surfaces is introduced in this paper this discrete conformality is shown to be computable it is proved that each hyperbolic polyhedral metric on a closed surface is discrete conformal to a unique hyperbolic polyhedral metric with a given discrete curvature satisfying gauss bonnet formula furthermore the hyperbolic polyhedral metric with given curvature can be obtained using a discrete yamabe flow with surgery in particular each hyperbolic polyhedral metric on a closed surface with negative euler characteristic is discrete conformal to a unique hyperbolic metric

the virtual cohomological dimension of the mapping class group of an orientable surface let f f r be the mapping class group of a surface f of genus g with s punctures and r boundary components the purpose of this paper is to establish cohomology properties of f parallel to those of the arithmetic groups if g is a linear algebraic group defined over q x is the symmetric space associated to g and a is an arithmetic subgroup of g then a is virtually torsion free and acts properly discontinuously on x the rational homology of a is the same as that of x a furthermore there is a bordification of x bs to a manifold with corners 3 and an extension of the action of a to a properly discontinuous action on jf so that the quotient x a is compact the boundary of jf is homotopy equivalent to a wedge of spheres say of dimension d and the virtual cohomological dimension of a is n d 1 where n is the dimension of x in the case of the mapping class group there is no analog for g ivanov unpublished has proven that f is not arithmetic nevertheless f acts properly discontinuously on teichmiiller space r which is homeomorphic to euclidean space of dimension 6 g 6 2 s 3 will play the role of the symmetric space the quotient of 9by f is the moduli space of curves whose rational homology is then identified with that of e harvey har has constructed a borel serre bordification j of 3 by analytic methods in the case where f has punctures we will build g by a different combinatorial method in addition we will explicitly describe inside y a cell complex y of dimension 4 g 4 s onto which j may be f equivariantly retracted thus establishing an analog of the constructions for sl n by serre soul6 sol and ash a this complex will be of the lowest possible dimension because we will use j to prove our main result

global uniqueness for a two dimensional semilinear elliptic inverse problem for a general class of nonlinear schrodinger equations au a x u 0 in a bounded planar domain 2 we show that the function a x u can be recovered from knowledge of the corresponding dirichlet to neumann map on the boundary dq

tiling the projective foliation space of a punctured surface there is a natural way to associate7 to each ideal triangulation of a punctured surface a cell decomposition of the projective foliation space of the punctured surface a recent theme in the topology of surfaces has been the special role played by punctured surfaces both in the study of geometric structures and in the study of measured foliations for example one important result has been the construction of an equivariant ideal cell decomposition of the teichmriller space of a punctured surface a result due to many people including harer strebel mumford epstein and bowditch and penner see for example har eb and p in all of these proofs an important construct has been an ideal cell division of the punctured surface indeed the cells of teichmuller space are in 1 1 correspondence with isotopy classes of ideal cell dirisions of the punctured surface in m1 and m2 ideal cell divisions were used in the study of measured foliations on a punctured surface in order to define conjugacy invariants of certain elements of the mapping class group of a punctured surface and to present an algorithm for computing these invariants it is the purpose of this work to provide a deeper foundation for the algorithm described in m1 in particular we shall develop the theory of measured foliations on a punctured surface from the ground up using the plan and several technical tools from flp but utilizing ideal triangulations in place of pairs of pants decompositions for actually constructing measured foliations our main result here is that to each isotopy class of ideal triangulations there is a naturally associated cell decompositiosn of b s thurston s space of projective measured foliations this result parallels the result of harer and penner that on any surface punctured or not to each choice of a pair of pants decomposition plus an additional choice of data sufficient to determine a marking of the surface there is a naturally associated cell decomposition of bs many of the techniques of proof used here are not new being adaptations and reorganizations of the techniques of flp the notable exception occurs in the use of elementary moves on ideal triangulations to understand the overlap maps of different parameterizations of xs rec eived by the editors may 25 1985 and in revised form april 3

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