3期

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
• 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, ...
• 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.
• 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.
• Supersingular K3 surfaces are unirational AI翻译
  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.
• M. Kontsevich's graph complex and the Grothendieck-Teichmuller Lie algebra AI翻译
  作者：Willwacher, Thomas
  作者单位：University of Zurich
  摘要：We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmuller Lie algebra . The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by , up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) operads may be expressed through the cohomology ...
• Badly approximable points on manifolds AI翻译
  作者：Beresnevich, Victor
  作者单位：University of York - UK
  摘要：This paper is motivated by two problems in the theory of Diophantine approximation, namely, Davenport's problem regarding badly approximable points on submanifolds of a Euclidean space and Schmidt's problem regarding the intersections of the sets of weighted badly approximable points. The problems have been recently settled in dimension two but remain open in higher dimensions. In this paper we develop new techniques that allow us to tackle them in full generality. The techniques rest on latti...
• An exact sequence for contact- and symplectic homology (vol 175, pg 611, 2009) AI翻译
  作者：Bourgeois, Frederic; Oancea, Alexandru
  作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
• Hypergraph containers AI翻译
  作者：Saxton, David; Thomason, Andrew
  作者单位：University of Cambridge
  摘要：We develop a notion of containment for independent sets in hypergraphs. For every -uniform hypergraph , we find a relatively small collection of vertex subsets, such that every independent set of is contained within a member of , and no member of is large; the collection, which is in various respects optimal, reveals an underlying structure to the independent sets. The containers offer a straightforward and unified approach to many combinatorial questions concerned (usually implicitly) with in...