Acta Mathematica

最新文章

• On Landau damping AI翻译
  作者：Mouhot, Clement; Villani, Cedric
  作者单位：University of Cambridge
  摘要：Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of regularity between kinetic and spatial variables, rather than exchanges of energy; phase mixing is the driving mechanism. The analysis involves new families of analytic norms, measuring regularity by comparison with solutions of the free transport equation;...
• Generalized Bafscklund-Darboux transformations for Coxeter-Toda flows from a cluster algebra perspective AI翻译
  作者：Gekhtman, Michael; Shapiro, Michael; Vainshtein, Alek
  作者单位：University of Notre Dame; Michigan State University; University of Haifa; University of Haifa
• A geometric approach to generalized Stokes conjectures AI翻译
  作者：Varvaruca, Eugen; Weiss, Georg S.
  作者单位：University of Reading; Heinrich Heine University Dusseldorf
  摘要：We consider the Stokes conjecture concerning the shape of extreme 2-dimensional water waves. By new geometric methods including a non-linear frequency formula, we prove the Stokes conjecture in the original variables. Our results do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity. Part of our results extends to the mathematical problem in higher dimensions.
• On locally constructible spheres and balls AI翻译
  作者：Benedetti, Bruno; Ziegler, Guenter M.
  作者单位：Free University of Berlin
  摘要：Durhuus and Jonsson (1995) introduced the class of locally constructible (LC) 3-spheres and showed that there are only exponentially many combinatorial types of simplicial LC 3-spheres. Such upper bounds are crucial for the convergence of models for 3D quantum gravity. We characterize the LC property for d-spheres (the sphere minus a facet collapses to a (d-2)-complex) and for d-balls. In particular, we link it to the classical notions of collapsibility, shellability and constructibility, and ...
• The endpoint case of the Bennett-Carbery-Tao multilinear Kakeya conjecture AI翻译
  作者：Guth, Larry
  作者单位：University of Toronto
  摘要：We prove the endpoint case of the multilinear Kakeya conjecture of Bennett, Carbery and Tao. The proof uses the polynomial method introduced by Dvir.
• Quantum cohomology of G/P and homology of affine Grassmannian AI翻译
  作者：Lam, Thomas; Shimozono, Mark
  作者单位：University of Michigan System; University of Michigan; Virginia Polytechnic Institute & State University
  摘要：Let G be a simple and simply-connected complex algebraic group, P aS,aEuro parts per thousand G a parabolic subgroup. We prove an unpublished result of D. Peterson which states that the quantum cohomology QH (*)(G/P) of a flag variety is, up to localization, a quotient of the homology H (*)(Gr (G) ) of the affine Grassmannian Gr (G) of G. As a consequence, all three-point genus-zero Gromov-Witten invariants of G/P are identified with homology Schubert structure constants of H (*)(Gr (G) ), est...
• Geodesics in large planar maps and in the Brownian map AI翻译
  作者：Le Gall, Jean-Francois
  作者单位：Universite Paris Saclay
  摘要：We study geodesics in the random metric space called the Brownian map, which appears as the scaling limit of large planar maps. In particular, we completely describe geodesics starting from the distinguished point called the root, and we characterize the set S of all points that are connected to the root by more than one geodesic. The set S is dense in the Brownian map and homeomorphic to a non-compact real tree. Furthermore, for every x in S, the number of distinct geodesics from x to the roo...
• Monge-Ampere equations in big cohomology classes AI翻译
  作者：Boucksom, Sebastien; Eyssidieux, Philippe; Guedj, Vincent; Zeriahi, Ahmed
  作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Aix-Marseille Universite
  摘要：We define non-pluripolar products of an arbitrary number of closed positive (1, 1)-currents on a compact Kahler manifold X. Given a big (1, 1)-cohomology class alpha on X (i.e. a class that can be represented by a strictly positive current) and a positive measure mu on X of total mass equal to the volume of alpha and putting no mass on pluripolar sets, we show that mu can be written in a unique way as the top-degree self-intersection in the non-pluripolar sense of a closed positive current in ...
• The Fourier spectrum of critical percolation AI翻译
  作者：Garban, Christophe; Pete, Gabor; Schramm, Oded
  作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); University of Toronto; Microsoft
• Estimates for maximal functions associated with hypersurfaces in R3 and related problems of harmonic analysis AI翻译
  作者：Ikromov, Isroil A.; Kempe, Michael; Mueller, Detlef
  作者单位：Samarkand State University; University of Kiel