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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：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：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：Gaidashev, Denis; Yampolsky, Michael
作者单位：Uppsala University; University of Toronto
摘要：In this paper we give a new proof of hyperbolicity of renormalization of critical circle maps using the formalism of almost-commuting pairs. We extend renormalization to two-dimensional dissipative maps of the annulus which are small perturbations of one-dimensional critical circle maps. Finally, we demonstrate that a two-dimensional map which lies in the stable set of the renormalization operator possesses attractor which is topologically a circle. Such a circle is critical: the dynamics on i...
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作者：Matomaki, Kaisa; Radziwill, Maksym; Tao, Terence
作者单位：University of Turku; California Institute of Technology; University of California System; University of California Los Angeles
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作者：Miller, Jason; Sheffield, Scott
作者单位：University of Cambridge; Massachusetts Institute of Technology (MIT)
摘要：Liouville quantum gravity (LQG) and the Brownian map (TBM) are two distinct models of measure-endowed random surfaces. LQG is defined in terms of a real parameter gamma, and it has long been believed that when gamma=8/3, the LQG sphere should be equivalent (in some sense) to TBM. However, the LQG sphere comes equipped with a conformal structure, and TBM comes equipped with a metric space structure, and endowing either one with the other's structure has been an open problem for some time. This ...
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作者：Hesselholt, Lars; Larsen, Michael; Lindenstrauss, Ayelet
作者单位：Nagoya University; University of Copenhagen; Indiana University System; Indiana University Bloomington
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作者：Bianchini, Stefano; Bonicatto, Paolo
作者单位：International School for Advanced Studies (SISSA)
摘要：Given a vector field.(1, b). L1 loc(R+ x Rd, Rd+1) such that divt, x(.(1, b)) is a measure, we consider the problem of uniqueness of the representation. of.(1, b)Ld+1 as a superposition of characteristics. : (t ., t +.). Rd,.. (t) = b(t,. (t)). We give conditions in terms of a local structure of the representation. on suitable sets in order to prove that there is a partition of Rd+1 into disjoint trajectories Pa, a. A, such that the PDE divt, x u.(1, b). M(Rd+1), u. L 8 (R+ x Rd), can be disin...
