recent progress on the poincare conjecture and the classification of 3 manifolds if m is a closed 3 manifold with trivial fundamental group then is m diffeomorphic to s the poincare conjecture is that the answer to this question is yes developing tools to attack this problem formed the basis for much of the work in 3 dimensional topology over the last century including for example the proof of dehn s lemma and the loop theorem and the study of surgery on knots and links in the 1980 s thurston developed another approach to 3 manifolds see 24 and 4 he considered 3 manifolds with riemannian metrics of constant negative curvature 1 these manifolds which are locally isometric to hyperbolic 3 space are called hyperbolic manifolds there are fairly obvious obstructions showing that not every 3 manifold can admit such a metric thurston formulated a general conjecture that roughly says that the obvious obstructions are the only ones should they vanish for a particular 3 manifold then that manifold admits such a metric his proof of various important special cases of this conjecture led him to formulate a more general conjecture about the existence of locally homogeneous metrics hyperbolic or otherwise for all manifolds this is called thurston s geometrization conjecture for 3 manifolds the statement of this conjecture is somewhat complicated so it is deferred until section 2 an important point is that thurston s geometrization conjecture includes the poincare conjecture as a very special case in addition thurston s conjecture has two advantages over the poincare conjecture it applies to all closed oriented 3 manifolds it posits a close relationship between topology and geometry in dimension three

simplical volume of closed locally symmetric spaces of non compact type we show that closed locally symmetric spaces of non compact type have positive simplicial volume this gives a positive answer to a question that was first raised by gromov in inst hautes etudes sci publ math 56 5 1982

minimal entropy and collapsing with curvature bounded from below we show that if a closed manifold m admits an structure not necessarily polarized possibly of rank zero then its minimal entropy vanishes in particular this is the case if m admits a non trivial s1 action as a corollary we obtain that the simplicial volume of a manifold admitting an structure is zero we also show that if m admits an structure then it collapses with curvature bounded from below this in turn implies that m collapses with bounded scalar curvature or equivalently its yamabe invariant is non negative we show that structures of rank zero appear rather frequently every compact complex elliptic surface admits one as well as any simply connected closed 5 manifold we use these results to study the minimal entropy problem we show the following two theorems suppose that m is a closed manifold obtained by taking connected sums of copies of s4 p2 overline mathbb c p 2 s2 s2and the k3 surface then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s4 p2 s2 s2 p2 overline mathbb c p 2 or p2 p2 finally suppose that m is a closed simply connected 5 manifold then m has zero minimal entropy moreover m admits a smooth riemannian metric with zero topological entropy if and only if m is diffeomorphic to s5 s3 s2 then on trivial s3 bundle over s2 or the wu manifold su 3 so 3

numerical taylor expansions for invariant manifolds we consider numerical computation of taylor expansions of invariant manifolds around equilibria of maps and flows these expansions are obtained by writing the corresponding functional equation in a number of points setting up a nonlinear system of equations and solving this system using a simplified newton s method this approach will avoid symbolic or explicit numerical differentiation the linear algebra issues of solving the resulting sylvester equations are studied in detail

a subdivision algorithm for the computation of unstable manifolds and global attractors each invariant set of a given dynamical system is part of the global attractor therefore the global attractor contains all the potentially interesting dynamics and in particular it contains every global unstable manifold for this reason it is of interest to have an algorithm which allows to approximate the global attractor numerically in this article we develop such an algorithm using a subdivision technique we prove convergence of this method in a very general setting and moreover we describe the qualitative convergence behavior in the presence of a hyperbolic structure the algorithm can successfully be applied to dynamical systems of moderate dimension and we illustrate this fact by several numerical examples

on long time evolution in general relativity and geometrization of 3 manifolds this paper introduces relations between the long time asymptotic behavior of einstein vacuum space times and the geometrization of 3 manifolds envisioned by thurston the relations are obtained by analysing the asymptotic behavior of a cmc foliation by compact cauchy surfaces and the induced curve of 3 manifold geometries the cheeger gromov theory is introduced in this context and a number of open problems are considered from this viewpoint

shear free relativistic fluids and the absence of movable branch points the problem of determining the metric for a nonstatic shear free spherically symmetric fluid either charged or neutral reduces to the problem of determining a one parameter family of solutions to a second order ordinary differential equation ode containing two arbitrary functions f and g choices for f and g are determined such that this ode admits a one parameter family of solutions that have poles as their only movable singularities this property is strictly weaker than the painleve property and it is used to identify classes of solvable models it is shown that this procedure systematically generates many exact solutions including the vaidya metric which does not arise from the standard painleve analysis of the second order ode interior solutions are matched to exterior reissner nordstrom metrics some solutions given in terms of second painleve transcendents are described

limits and degenerations of unitary conformal field theories in the present paper degeneration phenomena in conformal field theories are studied for this purpose a notion of convergent sequences of cfts is introduced properties of the resulting limit structure are used to associate geometric degenerations to degenerating sequences of cfts which as familiar from large volume limits of non linear sigma models can be regarded as commutative degenerations of the corresponding quantum geometries as an application the large level limit of the a series of unitary virasoro minimal models is investigated in detail in particular its geometric interpretation is determined

geometric structures gromov norm and kodaira dimensions abstract we define the kodaira dimension for 3 dimensional manifolds through thurston s eight geometries along with a classification in terms of this kodaira dimension we show this is compatible with other existing kodaira dimensions and the partial order defined by non zero degree maps for higher dimensions we explore the relations of geometric structures and mapping orders with various kodaira dimensions and other invariants especially we show that a closed geometric 4 manifold has nonvanishing gromov norm if and only if it has geometry h 2 h 2 h 2 c or h 4

all admissible meromorphic solutions of certain type of second degree second order algebraic odes abstract following the same idea of halburd and wang 9 to construct small functions of w and w by using the first one or two terms in the local series expansion for w at zeros we solve all the admissible meromorphic solutions of the second order algebraic differential equation w w w 2 a w w b w 2 w w where a b are constants and are small meromorphic functions of w in the sense of nevanlinna theory these solutions can have infinite order as hayman 11 has pointed out but still holds for his conjecture that t r w c 1 e c 2 r c 0 r when are rational functions where c 1 c 2 and c are some positive constants

metrics of negative ricci curvature one of the most natural and important topics in riemannian geometry is the relation between curvature and global structure of the underlying manifold for instance complete manifolds of negative sectional curvature are always aspherical and in the compact case their fundamental group can only contain abelian subgroups which are infinite cyclic furthermore it seemed to be a natural principle that a closed manifold cannot carry two metrics of different signed curvatures as it is a basic fact that this is true for sectional curvature but it turned out to be wrong much later and from a strongly analytic argument for the scalar curvature s since each manifold m n 3 admits a complete metric with s 1 cf aubin a and bland kalka bik hence the situation for ricci curvature ric lying between sectional and scalar curvature seemed to be quite delicate up to now the most general results concerning ric 0 were proved by gao yau gy and brooks br using thurston s theory of hyperbolic threemanifolds viz each closed three manifold admits a metric with ric 0 this is obtained from the fact that these manifolds carry hyperbolic metrics with certain singularities gao and yau resp brooks smoothed these singularities to get a regular metric with ric 0 these methods extend to three manifolds of finite type and certain hyperbolic orbifolds in any case the arguments rely on exploiting some extraordinary metric structures whose existence is neither obvious nor conceptually related to the ricci curvature problem indeed the existence depends on the assumption that the manifold is three dimensional and compact moreover this approach does not provide insight into the typical behaviour of metrics with ric 0 since one is led to very special metrics in this article we approach negative ricci curvature using a completely different and new concept which will become even more significant in l2 as we deliberately produce ric 0 actually we will prove the following results in these notes ric g resp r g denotes the ricci tensor resp curvature of a smooth metric g

collapsing manifolds obtained by kummer type constructions we construct f structures on a bott manifold and on some other manifolds obtained by kummer type constructions we also prove that if m e x where e is a fiber bundle with structure group g and a fiber admitting a g invariant metric of non negative sectional curvature and x admits an f structure with one trivial covering then one can construct on m a sequence of metrics with sectional curvature uniformly bounded from below and volume tending to zero i e vol k m 0 as a corollary we prove that all the elements in the spin cobordism ring can be represented by manifolds m with vol k m 0

collapsing with a lower bound on the curvature operator cheeger and gromov showed that f structures are related to collapse with a double sided curvature bound we define fibered f structures and extend some of the cheeger gromov results to the setting of collapse with a lower bound on the curvature operator

on the upper estimate of the heat kernel of a complete riemannian manifold let m be a complete non compact riemannian manifold whose sectional curvature is bounded between two constants k and k then one expects that the heat diffusion in such a manifold behaves like the heat diffusion in euclidean space the purpose of this paper is to give a justification of such a statement in 5 j cheeger and the third author found a lower estimate of the heat kernel by comparing it with the heat kernel of the space form whose curvature is the lower bound of the curvature of the manifold this lower estimate is sharp if we insist the dependence should be on the lower bound of the ricci curvature alone it remains to give an upper estimate of the heat kernel one does not however expect to have a comparison theorem for the upper bound because it is more sensitive to the geometry of the manifold in fact the heat kernel of the upper hialf space and the heat kernel of the complete hyperbolic manifold with finite volume have quite different behavior this is reflected by the fact that the laplacian has no discrete spectrum in the first case while infinite number of discrete eigenvalues may exist in the latter case what we will prove here is that in any case the heat kernel has to decay in a manner similar to the euclidean heat kernel thus we will prove that for any constant c 4 there exists c1 depending on c t the bound of the curvature of m and x so that for all t e 0 t

three manifolds with many flat planes we discuss the rigidity or lack thereof imposed by dierent no tions of having an abundance of zero curvature planes on a complete riemann ian 3 manifold we prove a rank rigidity theorem for complete 3 manifolds showing that having higher rank is equivalent to having reducible universal covering we also study 3 manifolds such that every tangent vector is con tained in a at plane including examples with irreducible universal covering and discuss the eect of nite volume and real analiticity assumptions

non singular solutions to the normalized ricci flow equation in this paper we study non singular solutions to ricci flow on a closed manifold of dimension at least 4 amongst other things we prove that if m is a closed 4 manifold on which the normalized ricci flow exists for all time t 0 with uniformly bounded sectional curvature then the euler characteristic chi m ge 0 moreover the 4 manifold satisfies one of the followings i m is a shrinking ricci soliton ii m admits a positive rank f structure iii the hitchin thorpe type inequality holds 2 chi m ge 3 tau m where chi m resp tau m is the euler characteristic resp signature of m

a concentration collapse decomposition for l2 flow singularities we exhibit a concentration collapse decomposition of singularities of fourth order curvature flows including the l2 curvature flow and calabi flow in dimensions n 4 the proof requires the development of several new a priori estimates first we develop a smoothing result for initial metrics with small energy and a volume growth lower bound in the vein of perelman s pseudolocality result next we generalize our technique from prior work to exhibit local smoothing estimates for the l2 flow in the presence of a curvature related bound a final key ingredient is a new local regularity result for l2 critical metrics with possibly nonconstant scalar curvature applications of these results include new compactness and diffeomorphism finiteness theorems for smooth compact 4 manifolds satisfying the necessary and effectively minimal hypotheses of l2 curvature pinching and a volume noncollapsing condition 2014 wiley periodicals inc

splittings and cr structures for manifolds with nonpositive sectional curvature let m n denote the universal covering space of a compact riemannian manifold m n with sectional curvature 1 k mn 0 we show that a collection of deck transformations of m n satisfying certain metric dependent conditions determines an open dense subset of m n at every point of which there exists a local isometric splitting with nontrivial flat factor such a collection which we call an abelian structure also gives rise to an essentially canonical cr structure in the sense of buyalo i e an atlas for an injective f structure for which additional conditions hold it follows in particular that the minimal volume of m n vanishes we show that an abelian structure exists if the injectivity radius at all points of m n is less than e n 0 this yields a conjecture of buyalo as well as a strengthened version of the conclusion of gromov s gap conjecture in our special situation in addition we observe that abelian structures on nonpositively curved manifolds have certain stability properties under suitably controlled changes of metric

collapsing and the differential form laplacian the case of a smooth limit space we analyze the limit of the p form laplacian under a collapse with bounded sectional curvature and bounded diameter to a smooth limit space as an application we characterize when the p form laplacian has small positive eigenvalues in a collapsing sequence

boundary regularity uniqueness and non uniqueness for ah einstein metrics on 4 manifolds abstract this paper studies several aspects of asymptotically hyperbolic ah einstein metrics mostly on 4 manifolds we prove boundary regularity at infinity for such metrics and establish uniqueness under natural conditions on the boundary data by examination of explicit black hole metrics it is shown that neither uniqueness nor finiteness holds in general for ah einstein metrics with a prescribed conformal infinity we then describe natural conditions which are sufficient to ensure finiteness

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

a boundary of the set of the riemannian manifolds with bounded curvatures and diameters on etudie la structure de la fermeture de l ensemble constitue par des classes d isometrie de varietes de riemann a courbures et diametres bornes

entropy and collapsing of compact complex surfaces we study the problem of existence of mathcal f structures in the sense of cheeger and gromov but not necessarily polarized on compact complex surfaces we give a complete classification of compact complex surfaces of kahler type admitting mathcal f structures in the non kahler case we give a complete classification modulo the gap in the classification of surfaces of class vii we then use these results to study the minimal entropy problem for compact complex surfaces we prove that modulo the gap in the classification of surfaces of class vii all compact complex surfaces of kodaira dimension less than or equal to 1 have minimal entropy zero and such a surface admits a smooth metric g with zero topological entropy if and only if it is mathbb c p 2 a ruled surface of genus 0 or 1 a hopf surface a complex torus a kodaira surface a hyperelliptic surface or a kodaira surface modulo a finite group the key result we use to prove this is a new topological obstruction to the existence of metrics with vanishing topological entropy finally we show that these results fit perfectly into wall s study of geometric structures on compact complex surfaces for instance we show that the minimal entropy problem can be solved for a minimal compact kahler surface s of kodaira dimension infty 0 or 1 if and only if s admits a geometric structure modelled on mathbb c p 2 s 2 times s 2 s 2 times mathbb e 2 or mathbb e 4

on the meromorphic solutions of an equation of hayman abstract the behavior of meromorphic solutions of differential equations has been the subject of much study research has concentrated on the value distribution of meromorphic solutions and their rates of growth the purpose of the present paper is to show that a thorough search will yield a list of all meromorphic solutions of a multi parameter ordinary differential equation introduced by hayman this equation does not appear to be integrable for generic choices of the parameters so we do not find all solutions only those that are meromorphic this is achieved by combining wiman valiron theory and local series analysis hayman conjectured that all entire solutions of this equation are of finite order all meromorphic solutions of this equation are shown to be either polynomials or entire functions of order one

the second twisted betti number and the convergence of collapsing riemannian manifolds let mi overset d gh longrightarrow x denote a sequence of n manifolds converging to a compact metric space x in the gromov hausdorff topology such that the sectional curvature is bounded in absolute value and dim x n we prove the following stability result if the fundamental groups of mi are torsion groups of uniformly bounded exponents and the second twisted betti numbers of mi vanish then there is a manifold m and a sequence of diffeomorphisms from m to a subsequence of mi such that the distance functions of the pullback metrics converge to a pseudo metric in c0 norm furthermore m admits a foliation with leaves diffeomorphic to flat manifolds not necessarily compact such that a vector is tangent to a leaf if and only if its norm converges to zero with respect to the pullback metrics these results lead to a few interesting applications

taylor approximation of invariant fiber bundles for nonautonomous difference equations abstract invariant fiber bundles generalize invariant manifolds to nonautonomous difference equations in this paper we develop a method to calculate their taylor approximation which is of crucial importance e g for an application of the reduction principle in a nonautonomous setting

on the fundamental groups of manifolds of positive sectional curvature let m be an n manifold with sectional curvature 0 6 k 1 the main result asserts that the fundamental group of m has a finite normal cyclic subgroup with index less than w n 8 oc a constant depending on n and 8

limits of random differential equations on manifolds consider a family of random ordinary differential equations on a manifold driven by vector fields of the form sum ky k alpha k z t epsilon omega where y k are vector fields epsilon is a positive number z t epsilon is a 1 over epsilon mathcal l 0 diffusion process taking values in possibly a different manifold alpha k are annihilators of mathrm ker mathcal l 0 under hormander type conditions on mathcal l 0 we prove that as epsilon approaches zero the stochastic processes y t over epsilon epsilon converge weakly and in the wasserstein topologies we describe this limit and give an upper bound for the rate of the convergence

critical riemannian 4 manifolds of m g and d is the volume element measured by g a critical point of sr g is called a critical metric on m that is the ricci tensor satisfies the critical equations grad srg 0 in particular for a compact 4 manifold m every einstein metric is a critical metric for sr on m recently gao g1 proved that the space of einstein metrics on a compact 4 manifold m has a certain compactness property in this paper we propose an extension of the compactness property for einstein metrics to critical metrics on a compact smooth riemannian 4 manifold m first we consider the subspace i m of all critical metrics on m with the injectivity radius bounded from below by a constant io 0 and diameter bounded from above by d then we are able to prove that i m is compact as a subset of moduli space of critical metrics in the ca topology more precisely we have the following theorem theorem a theorem 5 1 let i m be the subspace of all critical metrics on a compact 4 manifold m such that

numerical taylor expansions of invariant manifolds in large dynamical systems in this paper we develop a numerical method for computing higher order local approximations of invariant manifolds such as stable unstable or center manifolds near steady states of a dynamical system the underlying system is assumed to be large in the sense that a large sparse jacobian at the equilibrium occurs for which only a linear black box solver and a low dimensional invariant subspace is available but for which methods like the qr algorithm are considered to be too expensive our method is based on an analysis of the multilinear sylvester equations for the higher derivatives which can be solved under certain nonresonance conditions these conditions are weaker than the standard gap conditions on the spectrum which guarantee the existence of the invariant manifold the final algorithm requires the solution of several large linear systems with a bordered jacobian to these systems we apply a block elimination method recently developed by govaerts and pryce 12 14

classification of meromorphic integrals for autonomous nonlinear ordinary differential equations with two dominant monomials abstract the nevanlinna theory is used to derive the general structure of transcendental meromorphic solutions for a wide class of autonomous nonlinear ordinary differential equations with two dominant monomials an algebro geometric method which enables one to obtain these solutions explicitly is described new simply periodic solutions of the lorenz system are obtained

collapsing riemannian manifolds to ones of lower dimensions on considere l effondrement d une suite de varietes de riemann mi vers un espace de dimension inferieure x on etudie le cas ou l espace limite x est une variete de riemann et les courbures sectionnelles de mi sont bornees

volume collapsed three manifolds with a lower curvature bound in this paper we determine the topology of three dimensional complete orientable riemannian manifolds with a uniform lower bound of sectional curvature whose volume is sufficiently small

rationality of geometric signatures of complete 4 manifolds according to cg4 and cfg the complete manifolds with bounded sectional curvature and finite volume admit positive rank f structures near infinity in this paper we show that in dimension four if the manifolds also have bounded covering geometry near infinity then there exist f structures with special topological properties f structures with these properties cannot be constructed solely by means of the general methods in cg4 and cfg using these special properties we prove a conjecture of cheeger gromov on the rationality of the geometric signatures in the four dimensional case

a mass for alf manifolds we prove a positive mass theorem on alf manifolds i e complete noncompact manifolds that are asymptotic to a circle fibration over a euclidean base with fibers of asymptotically constant length

ends of finite volume nonpositively curved manifolds we study complete finite volume n manifolds m of bounded nonpositive sectional curvature a classical theorem of m gromov says that if such m has negative curvature then it is homeomorphic to the interior of a compact manifold with boundary and we denote this boundary partial m if n ge 3 we prove that the universal cover of the boundary widetilde partial m and also the pi 1m cover of the boundary partial widetilde m have vanishing n 2 dimensional homology for n 4 the first of these recovers a result of nguy tilde hat mathrm e n phan saying that each component of the boundary partial m is aspherical for any n ge 3 the second of these implies the vanishing of the first group cohomology group with group ring coefficients h 1 b pi 1m mathbb z pi 1m 0 a consequence is that pi 1m is freely indecomposable these results extend to manifolds m of bounded nonpositive curvature if we assume that m is homeomorphic to the interior of a compact manifold with boundary our approach is a form of homological collapse for ends of finite volume manifolds of bounded nonpositive curvature this paper is very much influenced by earlier yet still unpublished work of nguy tilde hat mathrm e n phan

collapsing riemannian manifolds while keeping their curvature bounded i soit y n une variete de riemann connexe complete et p y n le rayon d injectivite i p de l application exponentielle en p est defini comme etant le plus petit r tel que exp p b r p n est pas un diffeomorphisme sur son image on etudie la situation dans laquelle la taille du rayon d injectivite est petite relativement a la courbure

the uniqueness of the measure of maximal entropy for geodesic flows on rank 1 manifolds in this paper we prove a conjecture of a katok stating that the geodesic flow on a compact rank 1 manifold admits a uniquely determined invariant measure of maximal entropy this generalizes previous work of r bowen and g margulis as an application we show that the exponential growth rate of the set of singular closed geodesics is strictly smaller than the topological entropy

removing point singularities of riemannian manifolds we study the behavior of geodesics passing through a point singularity of a riemannian manifold in particular we show that if the curvature does not blow up too rapidly near the singularity then the singularity is at worst an orbifold singularity the idea is to construct the exponential map centered at a singularity since there is no tangent space at the singularity a surrogate is needed we show that the vector space of radially parallel vector fields is well defined and that there is a correspondence between unit radially parallel vector fields and geodesics emanating from the singular point

computation of nonautonomous invariant and inertial manifolds we derive a numerical scheme to compute invariant manifolds for time variant discrete dynamical systems i e nonautonomous difference equations our universally applicable method is based on a truncated lyapunov perron operator and computes invariant manifolds using a system of nonlinear algebraic equations which can be solved both locally using nonsmooth inexact newton and globally using continuation algorithms compared to other algorithms our approach is quite flexible since it captures time dependent nonsmooth noninvertible or implicit equations and enables us to tackle the full hierarchy of strongly stable stable and center stable manifolds as well as their unstable counterparts our results are illustrated using a test example and are applied to a population dynamical model and the henon map finally we discuss a linearly implicit euler bubnov galerkin discretization of a reaction diffusion equation in order to approximate its inertial manifold

monodromy preserving deformation of linear ordinary differential equations with rational coefficients iii abstract a unified treatment of monodromy and spectrum preserving deformations is presented in particular a general procedure is described to reduce the latter into the former consistently the concept of the function previously introduced for the former 2 is extended to the isospectral context it is shown that the general monodromy and spectrum preserving deformation equations can be written as hirota s bilinear differential equations by using the functions as dependent variables

structure of manifolds of nonpositive curvature clearly 1 rank m dim m we may regard rank m as a measurement of the flatness of m since a parallel field x along yv and perpendicular to yv is a jacobi field if and only if the sectional curvatures of the planes i t a x t are zero for all t e r in particular m is flat if rank m dim m hence a compact surface of nonpositive curvature has rank one unless it is a torus or a klein bottle it also follows that rank m1 x m2 rank ml rank m2 finally it is important that the definition of rank m above coincides with the usual one if m is locally symmetric

vanishing of cohomology groups and large eigenvalues of the laplacian on p forms for collapsing of closed riemannian manifolds the first positive eigenvalue of the laplacian on p forms may or may not tend to infinity in special cases we show that the existence of the first positive eigenvalue tending to infinity is related to vanishing of cohomology groups of generic fibers

nilpotent structures and invariant metrics on collapsed manifolds let mn be a complete riemannian manifold of bounded curvature say iki 0 we put mn w n c u fn c where 1n e consists of those points at which the injectivity radius of the exponential map is e the complementary set n c is called the e collapsed part of mn if x e 4 n r e then the metric ball bx r is quasi isometric with small distortion to the flat ball b0 r in the euclidean space rn after slightly

collapsing of abelian fibered calabi yau manifolds we study the collapsing behavior of ricci flat kahler metrics on a projective calabi yau manifold which admits an abelian fibration when the volume of the fibers approaches zero we show that away from the critical locus of the fibration the metrics collapse with locally bounded curvature and along the fibers the rescaled metrics become flat in the limit the limit metric on the base minus the critical locus is locally isometric to an open dense subset of any gromov hausdorff limit space of the ricci flat metrics we then apply these results to study metric degenerations of families of polarized hyperkahler manifolds in the large complex structure limit in this setting we prove an analogue of a result of gross and wilson for k3 surfaces which is motivated by the strominger yau zaslow picture of mirror symmetry