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作者：Li, Chao
作者单位：Stanford University
摘要：The study of comparison theorems in geometry has a rich history. In this paper, we establish a comparison theorem for polyhedra in 3-manifolds with nonnegative scalar curvature, answering affirmatively a dihedral rigidity conjecture by Gromov. For a large collections of polyhedra with interior non-negative scalar curvature and mean convex faces, we prove the dihedral angles along its edges cannot be everywhere less or equal than those of the corresponding Euclidean model, unless it is isometri...
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作者：Ou, Dyi-Shing
作者单位：State University of New York (SUNY) System; Stony Brook University; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：This article generalizes the nonexistence of wandering domains from unimodal maps to infinitely period-doubling renormalizable Henon-like maps in the strongly dissipative (area contracting) regime. This solves an open problem proposed by van Strien (Discrete Contin Dyn Syst 27(2):557-588, 2010) and Lyubich and Martens (Invent Math 186(1):115-189, 2011). We partition the phase space of a Henon-like map into two regions: the good region and the bad region. The good region is where the method of ...
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作者：Ntalampekos, Dimitrios; Younsi, Malik
作者单位：State University of New York (SUNY) System; Stony Brook University; University of Hawaii System; University of Hawaii Manoa
摘要：A circle domain omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega $$\end{document} in the Riemann sphere is conformally rigid if every conformal map from omega\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
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作者：Azzam, Jonas; Hofmann, Steve; Maria Martell, Jose; Mourgoglou, Mihalis; Tolsa, Xavier
作者单位：University of Edinburgh; University of Missouri System; University of Missouri Columbia; Consejo Superior de Investigaciones Cientificas (CSIC); CSIC - Instituto de Ciencia de Materiales de Madrid (ICMM); CSIC - Instituto de Ciencias Matematicas (ICMAT); University of Basque Country; Basque Foundation for Science; ICREA; Autonomous University of Barcelona; Autonomous University of Barcelona
摘要：It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak-A(infinity) property) of harmonic measure with respect to surface measure, on the boundary of an open set Omega subset of Rn+1 with Ahlfors-David \regular boundary, is equivalent to the solvability of the Dirichlet problem in Omega, with data in L-p(partial derivative Omega) for some p < infinity. In this paper, we give a geometric characterization of the weak-A(infinity) property, of harmonic mea...
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作者：Groechenig, Michael; Wyss, Dimitri; Ziegler, Paul
作者单位：University of Toronto; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Technical University of Munich
摘要：We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type SLn and PGL(n). More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore, we prove for...
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作者：Mellit, Anton
作者单位：University of Vienna
摘要：Using our earlier results on polynomiality properties of plethystic logarithms of generating series of certain type, we show that Schiffmann's formulas for various counts of Higgs bundles over finite fields can be reduced to much simpler formulas conjectured by Mozgovoy. In particular, our result implies the conjecture of Hausel and Rodriguez-Villegas on the Poincare polynomials of twisted character varieties and the conjecture of Hausel and Thaddeus on independence of E-polynomials on the deg...
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作者：King, Alastair; Qiu, Yu
作者单位：University of Bath; Tsinghua University
摘要：We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the universal cover of this groupoid can be constructed using the covering graph of triangulations of the surface with extra decorations. This covering graph is a skeleton for a space of...
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作者：Alper, Jarod; Blum, Harold; Halpern-Leistner, Daniel; Xu, Chenyang
作者单位：University of Washington; University of Washington Seattle; Utah System of Higher Education; University of Utah; Cornell University; Massachusetts Institute of Technology (MIT)
摘要：We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and Theta-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a separated good moduli space.
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作者：Danciger, Jeffrey; Maloni, Sara; Schlenker, Jean-Marc
作者单位：University of Texas System; University of Texas Austin; University of Virginia; University of Luxembourg
摘要：We study convex polyhedra in three-space that are inscribed in a quadric surface. Up to projective transformations, there are three such surfaces: the sphere, the hyperboloid, and the cylinder. Our main result is that a planar graph Gamma is realized as the 1-skeleton of a polyhedron inscribed in the hyperboloid or cylinder if and only if Gamma is realized as the 1-skeleton of a polyhedron inscribed in the sphere and Gamma admits a Hamiltonian cycle. This answers a question asked by Steiner in...
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作者：Brown, Aaron; Fisher, David; Hurtado, Sebastian
作者单位：University of Chicago; Indiana University System; Indiana University Bloomington
摘要：We prove Zimmer's conjecture for C2 actions by finite-index subgroups of SL(m, Z) provided m > 3. The method utilizes many ingredients from our earlier proof of the conjecture for actions by cocompact lattices in SL(m, R) (Brown et al. in Zimmer's conjecture: subexponential growth, measure rigidity, and strong property (T), 2016. arXiv:1608.04995) but new ideas are needed to overcome the lack of compactness of the space (G x M)/ (admitting the induced G-action). Non-compactness allows both mea...
