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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.
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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, ...
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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...
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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.
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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...
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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.
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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...
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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.
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作者：Bourgain, Jean; Li, Dong
作者单位：Institute for Advanced Study - USA; University of British Columbia
摘要：For the -dimensional incompressible Euler equation, the standard energy method gives local wellposedness for initial velocity in Sobolev space , . The borderline case was a folklore open problem. In this paper we consider the physical dimension and show that if we perturb any given smooth initial data in norm, then the corresponding solution can have infinite norm instantaneously at . In a companion paper [1] we settle the 3D and more general cases. The constructed solutions are unique and eve...
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作者：Liedtke, Christian
作者单位：Technical University of Munich
摘要：We show that supersingular K3 surfaces in characteristic are related by purely inseparable isogenies. This implies that they are unirational, which proves conjectures of Artin, Rudakov, Shafarevich, and Shioda. As a byproduct, we exhibit the moduli space of rigidified K3 crystals as an iterated -bundle over . To complete the picture, we also establish Shioda-Inose type isogeny theorems for K3 surfaces with Picard rank in positive characteristic.
