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• A mass transportation approach to quantitative isoperimetric inequalities AI翻译
  作者：Figalli, A.; Maggi, F.; Pratelli, A.
  作者单位：University of Texas System; University of Texas Austin; University of Florence; University of Pavia
  摘要：A sharp quantitative version of the anisotropic isoperimetric inequality is established, corresponding to a stability estimate for the Wulff shape of a given surface tension energy. This is achieved by exploiting mass transportation theory, especially Gromov's proof of the isoperimetric inequality and the Brenier-McCann Theorem. A sharp quantitative version of the Brunn-Minkowski inequality for convex sets is proved as a corollary.
• The Rost nilpotence theorem for geometrically rational surfaces AI翻译
  作者：Gille, Stefan
  作者单位：University of Munich
  摘要：We show that the Rost nilpotence theorem is true for geometrically rational surfaces over fields of characteristic zero.
• Gross-Schoen cycles and dualising sheaves AI翻译
  作者：Zhang, Shou-Wu
  作者单位：Columbia University
• Fredholm properties of Riemannian exponential maps on diffeomorphism groups AI翻译
  作者：Misiolek, Gerard; Preston, Stephen C.
  作者单位：University of Colorado System; University of Colorado Boulder; University of Notre Dame
  摘要：We prove that exponential maps of right-invariant Sobolev H (r) metrics on a variety of diffeomorphism groups of compact manifolds are nonlinear Fredholm maps of index zero as long as r is sufficiently large. This generalizes the result of Ebin et al. (Geom. Funct. Anal. 16, 2006) for the L (2) metric on the group of volume-preserving diffeomorphisms important in hydrodynamics. In particular, our results apply to many other equations of interest in mathematical physics. We also prove an infini...
• Well-posedness of the transport equation by stochastic perturbation AI翻译
  作者：Flandoli, F.; Gubinelli, M.; Priola, E.
  作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite PSL; Universite Paris-Dauphine; University of Pisa; University of Turin
  摘要：We consider the linear transport equation with a globally Holder continuous and bounded vector field, with an integrability condition on the divergence. While uniqueness may fail for the deterministic PDE, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of a PDE of fluid dynamics that becomes well-posed under the influence of a (multiplicative) noise. The key tool is a differentiabl...
• A complete characterization of coefficients of a.e. convergent orthogonal series and majorizing measures AI翻译
  作者：Paszkiewicz, Adam
  作者单位：University of Lodz
  摘要：We characterize sequences of numbers (a (n) ) such that a (na parts per thousand yen1) a (n) I broken vertical bar (n) converges a.e. for any orthonormal system (I broken vertical bar (n) ) in any L (2)-space. In our criteria we use the set A={a (ma parts per thousand yenn|)|a (m) |(2);na parts per thousand yen1}, majorizing measures on A, and new descriptions of the complexity of A.
• Fake projective planes (vol 168, pg 321, 2007) AI翻译
  作者：Prasad, Gopal; Yeung, Sai-Kee
  作者单位：University of Michigan System; University of Michigan; Purdue University System; Purdue University
• Categorical geometric skew Howe duality AI翻译
  作者：Cautis, Sabin; Kamnitzer, Joel; Licata, Anthony
  作者单位：University of Toronto; Stanford University; Columbia University
  摘要：We categorify the R-matrix isomorphism between tensor products of minuscule representations of U-q (sl(n)) by constructing an equivalence between the derived categories of coherent sheaves on the corresponding convolution products in the affine Grassmannian. The main step in the construction is a categorification of representations of U-q (sl(2)) which are related to representations of U-q (sl(n)) by quantum skew Howe duality. The resulting equivalence is part of the program of algebro-geometr...
• Representation of certain homogeneous Hilbertian operator spaces and applications AI翻译
  作者：Junge, Marius; Xu, Quanhua
  作者单位：Universite Marie et Louis Pasteur; University of Illinois System; University of Illinois Urbana-Champaign
  摘要：Following Grothendieck's characterization of Hilbert spaces we consider operator spaces F such that both F and F* completely embed into the dual of a C*-algebra. Due to Haagerup/Musat's improved version of Pisier/Shlyakhtenko's Grothendieck inequality for operator spaces, these spaces are quotients of subspaces of the direct sum C circle plus R of the column and row spaces (the corresponding class being denoted by QS(C circle plus R)). We first prove a representation theorem for homogeneous F ...
• Orbit equivalence for Cantor minimal acurrency sign d -systems AI翻译
  作者：Giordano, Thierry; Matui, Hiroki; Putnam, Ian F.; Skau, Christian F.
  作者单位：Chiba University; University of Ottawa; University of Victoria; Norwegian University of Science & Technology (NTNU)
  摘要：We show that every minimal action of any finitely generated abelian group on the Cantor set is (topologically) orbit equivalent to an AF relation. As a consequence, this extends the classification up to orbit equivalence of minimal dynamical systems on the Cantor set to include AF relations and acurrency sign (d) -actions.