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作者：Costa, Ivan Sadofschi
作者单位：University of Buenos Aires
摘要：In this series of two articles, we prove that every action of a finite group G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} on a finite and contractible 2-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the acyclic 2-dimensi...
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作者：McDuff, Dusa; Siegel, Kyler
摘要：We show that the infinite staircases which arise in the ellipsoid embedding functions of rigid del Pezzo surfaces (with their monotone symplectic forms) can be entirely explained in terms of rational sesquicuspidal symplectic curves. Moreover, we show that these curves can all be realized algebraically, giving various new families of algebraic curves with one cusp singularity. Our main techniques are (i) a generalized Orevkov twist, and (ii) the interplay between algebraic & Qopf;-Gorenstein s...
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作者：Benoist, Olivier
作者单位：Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a comparison theorem between the & eacute;tale cohomology of algebraic varieties over Stein compacta and the singular cohomology of their analytifications. We deduce that the field of meromorphic functions in a neighborhood of a connected Stein compact subset of a normal complex space of dimension n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{...
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作者：Becker, Lars; Klein, Ohad; Slote, Joseph; Volberg, Alexander; Zhang, Haonan
作者单位：University of Bonn; Hebrew University of Jerusalem; California Institute of Technology; Michigan State University; University of Bonn; University of South Carolina System; University of South Carolina Columbia
摘要：Let f\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f$\end{document} be an analytic polynomial of degree at most K-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemar...
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作者：Milman, Emanuel; Shabelman, Shahar; Yehudayoff, Amir
作者单位：Technion Israel Institute of Technology; University of Copenhagen
摘要：The intersection body I K of a star body K in R-n was introduced by E. Lutwak following the work of H. Busemann, and plays a central role in the dual Brunn-Minkowski theory. We show that when n >= 3, (IK)-K-2=cK iff K is a centered ellipsoid, and hence I K = c K iff K is a centered Euclidean ball, answering long-standing questions by Lutwak, Gardner, and Fish-Nazarov-Ryabogin-Zvavitch. An equivalent formulation of the latter in terms of non-linear harmonic analysis states that a non-negative r...
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作者：Logunov, A.; Malinnikova, E.; Nadirashvili, N.; Nazarov, F.
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
摘要：Consider a solution u to Delta u + Vu = 0 on R-2, where V is real-valued, measurable and |V|<= 1. If |u(x)| <= exp (-C|x|log(1/2)|x|), |x| > 2, where C is a sufficiently large absolute constant, then u equivalent to 0.
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作者：Heinavaara, Otte
作者单位：Princeton University
摘要：Given two Hermitian matrices, A and B, we introduce a new type of spectral measure, a tracial joint spectral measure mu A, B on the plane. Existence of this measure implies the following two results: 1) any two-dimensional subspace of the Schatten-p class is isometric to a subspace of Lp, and 2) if f : R R has non-negative kth derivative and A and B are Hermitian matrices with A positive semidefinite, then t trf (tA + B) has non-negative kth derivative. We also give an explicit expression for ...
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作者：Gerber, Marlies; Kunde, Philipp
作者单位：Indiana University System; Indiana University Bloomington; Jagiellonian University; Oregon State University
摘要：A time change of a flow {Tt}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{T_{t}\}$\end{document}, t is an element of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsi...
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作者：Budzinski, Thomas; Curien, Nicolas; Petri, Bram
作者单位：Centre National de la Recherche Scientifique (CNRS); Ecole Normale Superieure de Lyon (ENS de LYON); Universite Paris Saclay; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France
摘要：It is a well-known result due to Bollob & aacute;s that the maximal Cheeger constant of large d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$d$\end{document}-regular graphs cannot be close to the Cheeger constant of the d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} ...
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作者：Martin, Daniel E.
作者单位：Clemson University
摘要：In 2021, Chen proved that the size of any connected component of the Markoff mod p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p$\end{document} graph is divisible by p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{...
