-
作者：Luhrmann, Jonas; Oh, Sung-Jin; Shahshahani, Sohrab
作者单位：Texas A&M University System; Texas A&M University College Station; University of California System; University of California Berkeley; Korea Institute for Advanced Study (KIAS); University of Massachusetts System; University of Massachusetts Amherst
摘要：We study the problem of stability of the catenoid, which is an asymptotically flat rotationally symmetric minimal surface in Euclidean space, viewed as a stationary solution to the hyperbolic vanishing mean curvature equation in Minkowski space. The latter is a quasilinear wave equation that constitutes the hyperbolic counterpart of the minimal surface equation in Euclidean space. Our main result is the nonlinear asymptotic stability, modulo suitable translation and boost (i.e., modulation), o...
-
作者：Armstrong, Scott; Kuusi, Tuomo
作者单位：New York University; University of Helsinki
摘要：We prove a quantitative estimate for the homogenization length scale in terms of the ellipticity ratio Lambda/lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Lambda /\lambda $\end{document} of the coefficient field. This upper bound applies to high-contrast elliptic equations exhibiting near-critical behavior...
-
作者：Cohen, Alex; Pohoata, Cosmin; Zakharov, Dmitrii
作者单位：Massachusetts Institute of Technology (MIT); Emory University
摘要：Let p1,& mldr;,pn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p_{1},\ldots ,p_{n}$\end{document} be a set of points in the unit square and let T1,& mldr;,Tn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \...
-
作者：Regeta, Andriy; Urech, Christian; van Santen, Immanuel
作者单位：University of Padua; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Basel
摘要：Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} be an irreducible variety and Bir(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt}...
-
作者：Abdurrahman, Amina; Venkatesh, Akshay
作者单位：Princeton University; Institute for Advanced Study - USA
摘要：We propose (and prove under some restrictions) that the square class of the central value of the L-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.
-
作者：Hassainia, Zineb; Hmidi, Taoufik; Masmoudi, Nader
作者单位：New York University; New York University Abu Dhabi; New York University
摘要：This paper investigates the leapfrogging phenomenon in inviscid planar flows, specifically for the 2D Euler equations, showing that under suitable constraints, four concentrated vortex patches leapfrog indefinitely. Observing this system from a translating reference frame reveals a non-rigid time-periodic motion of the vortex patches. These solutions are shown to evolve near singular time-periodic relative equilibria of the point vortex system. Our proof hinges upon two main components. First,...
-
作者：Guichard, Olivier; Wienhard, Anna
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Max Planck Society
摘要：We introduce the notion of Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Theta $\end{document}-positivity in real semisimple Lie groups. This notion at the same time generalizes Lusztig's total positivity in split real Lie groups and invariant orders in Lie groups of Hermitian type. We show that there are fo...
-
作者：Osajda, Damian; Przytycki, Piotr
作者单位：University of Wroclaw; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; McGill University
摘要：We prove that Coxeter groups are biautomatic. From our construction of the biautomatic structure it follows that uniform lattices in isometry groups of buildings are biautomatic.
-
作者：Lim, Willie Rush
作者单位：Brown University
摘要：By adapting the near-degenerate regime designed by Kahn, Lyubich, and D. Dudko, we prove that the boundaries of Herman rings with bounded type rotation number and of the simplest configuration are quasicircles with dilatation depending only on the degree and the rotation number. As a consequence, we show that these Herman rings always degenerate to a Herman curve, i.e. an invariant Jordan curve that is not contained in the closure of a rotation domain and on which the map is conjugate to a rig...
-
作者：Li, Yangyang; Wang, Zhihan
作者单位：University of Chicago
摘要：We show that in an 8-dimensional closed Riemmanian manifold with Cam-generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic regularity conjecture of minimal hypersurfaces in dimension eight. This also enables us to generalize many generic geometric properties of (Almgren-Pitts) min-max minimal hypersurfaces, previously only known in low dimensions, to dimension eight. En route to our main results, we have proved a sheeting theorem for minimal hype...
