-
作者：Hahn, Jeremy; Shi, XiaoLin Danny
作者单位：Massachusetts Institute of Technology (MIT); University of Chicago
摘要：We show that Lubin-Tate spectra at the prime 2 are Real oriented and Real Landweber exact. The proof is by application of the Goerss-Hopkins-Miller theorem to algebras with involution. For each height n, we compute the entire homotopy fixed point spectral sequence for E-n with its C-2-action given by the formal inverse. We study, as the height varies, the Hurewicz images of the stable homotopy groups of spheres in the homotopy of these C-2-fixed points.
-
作者：Figalli, Alessio; Serra, Joaquim
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove that every bounded stable solution of (-Delta)1/2u+f(u)=0 in R3 is a 1D profile, i.e., u(x)=phi(e center dot x) for some e is an element of S2, where phi:R -> R is a nondecreasing bounded stable solution in dimension one. Equivalently, stable critical points of boundary reaction problems in R+d+1=Rd+1 boolean AND{xd+1 >= 0} of the form {xd+1 >= 0}12| are 1D when d=3 These equations have been studied since the 1940's in crystal dislocations. Also, as it happens for the Allen-Cahn equat...
-
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...
-
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 ...
-
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{...
-
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...
-
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...
-
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...
-
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...
-
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.
