2015

最新文章

• Infinitely many monotone Lagrangian tori in R6 AI翻译
  作者：Auroux, Denis
  作者单位：University of California System; University of California Berkeley
  摘要：We construct infinitely many families of monotone Lagrangian tori in , no two of which are related by Hamiltonian isotopies (or symplectomorphisms). These families are distinguished by the (arbitrarily large) numbers of families of Maslov index 2 pseudo-holomorphic discs that they bound.
• Hyperbolicity of generic high-degree hypersurfaces in complex projective space AI翻译
  作者：Siu, Yum-Tong
  作者单位：Harvard University
• Universal Gauss-Thakur sums and L-series AI翻译
  作者：Angles, Bruno; Pellarin, Federico
  作者单位：Universite de Caen Normandie; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：We prove that the maximal abelian extension tamely ramified at infinity of the rational function field over is generated by the values at the points in the algebraic closure of of the higher derivatives of the so-called Anderson and Thakur function We deduce a similar property for the special values of the higher derivatives of a new kind of -series introduced by the second author.
• Global solutions for the gravity water waves system in 2d AI翻译
  作者：Ionescu, Alexandru D.; Pusateri, Fabio
  作者单位：Princeton University
  摘要：We consider the gravity water waves system in the case of a one dimensional interface, for sufficiently smooth and localized initial data, and prove global existence of small solutions. This improves the almost global existence result of Wu (Invent Math 177(1): 45-135, 2009). We also prove that the asymptotic behavior of solutions as time goes to infinity is different from linear, unlike the three dimensional case (Germain et al., Ann Math 175(2):691-754, 2012; Wu, Invent Math 184(1):125-220, ...
• The bounded curvature conjecture AI翻译
  作者：Klainerman, Sergiu; Rodnianski, Igor; Szeftel, Jeremie
  作者单位：Princeton University; Universite PSL; Ecole Normale Superieure (ENS)
  摘要：This is the main paper in a sequence in which we give a complete proof of the bounded curvature conjecture. More precisely we show that the time of existence of a classical solution to the Einstein-vacuum equations depends only on the -norm of the curvature and a lower bound on the volume radius of the corresponding initial data set. We note that though the result is not optimal with respect to the scaling of the Einstein equations, it is nevertheless critical with respect to its causal geomet...
• On the equivalence of the entropic curvature-dimension condition and Bochner's inequality on metric measure spaces AI翻译
  作者：Erbar, Matthias; Kuwada, Kazumasa; Sturm, Karl-Theodor
  作者单位：University of Bonn; Institute of Science Tokyo; Tokyo Institute of Technology
  摘要：We prove the equivalence of the curvature-dimension bounds of Lott-Sturm-Villani (via entropy and optimal transport) and of Bakry-A parts per thousand mery (via energy and -calculus) in complete generality for infinitesimally Hilbertian metric measure spaces. In particular, we establish the full Bochner inequality on such metric measure spaces. Moreover, we deduce new contraction bounds for the heat flow on Riemannian manifolds and on mms in terms of the -Wasserstein distance.
• Construction of the Witten-Reshetikhin-Turaev TQFT from conformal field theory AI翻译
  作者：Andersen, Jorgen Ellegaard; Ueno, Kenji
  作者单位：Aarhus University; Hosei University
  摘要：In Andersen and Ueno (J Knot Theory Ramif 16:127-202, 2007) we constructed the vacua modular functor based on the sheaf of vacua theory developed in Tsuchiya et al. (Adv Stud Pure Math 19:459-566, 1989) and the abelian analog in Andersen and Ueno (Int J Math 18:919-993, 2007). We here provide an explicit isomorphism from the modular functor underlying the skein-theoretic model for the Witten-Reshetikhin-Turaev TQFT due to Blanchet, Habbeger, Masbaum and Vogel to the vacua modular functor. This...
• Generic hyperbolicity of Aubry sets on surfaces AI翻译
  作者：Contreras, G.; Figalli, A.; Rifford, L.
  作者单位：University of Texas System; University of Texas Austin; Universite Cote d'Azur
  摘要：Given a Tonelli Hamiltonian of class on the cotangent bundle of a compact surface, we show that there is an open dense set of potentials in the topology for which the Aubry set is hyperbolic in its energy level.
• Lattices in the cohomology of Shimura curves AI翻译
  作者：Emerton, Matthew; Gee, Toby; Savitt, David
  作者单位：University of Chicago; Imperial College London; University of Arizona
  摘要：We prove the main conjectures of Breuil (J Reine Angew Math, 2012) (including a generalisation from the principal series to the cuspidal case) and Demb,l, (J Reine Angew Math, 2012), subject to a mild global hypothesis that we make in order to apply certain theorems. More precisely, we prove a multiplicity one result for the mod cohomology of a Shimura curve at Iwahori level, and we show that certain apparently globally defined lattices in the cohomology of Shimura curves are determined by the...
• Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type AI翻译
  作者：Straube, Emil J.; Zeytuncu, Yunus E.
  作者单位：Texas A&M University System; Texas A&M University College Station; University of Michigan System; University of Michigan
  摘要：Let be a pseudoconvex, oriented, bounded and closed CR submanifold of of hypersurface type. Our main result says that when a certain -form on is exact on the null space of the Levi form, then the complex Green operator on satisfies Sobolev estimates. This happens in particular when admits a set of plurisubharmonic defining functions or when is strictly pseudoconvex except for the points on a simply connected complex submanifold.