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作者：Polimeni, Davide; Terracini, Susanna
作者单位：University of Turin
摘要：We deal, for the classical N-body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic, hyperbolic-parabolic and parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action on a suitable functional space. With this new strategy, we are able to confirm the already-known results of the existence of both h...
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作者：Bordenave, Charles; Collins, Benoit
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Kyoto University
摘要：Voiculescu discovered asymptotic freeness of independent Haar-distributed unitary matrices. Many refinements have been obtained, including strong asymptotic freeness of random unitaries and strong asymptotic freeness of random permutations acting on the orthogonal of the Perron-Frobenius eigenvector. In this paper, we consider a new matrix unitary model appearing naturally from representation theory of compact groups. We fix a nontrivial signature rho\documentclass[12pt]{minimal} \usepackage{a...
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作者：Liu, Yuan; Wood, Melanie Matchett; Zureick-Brown, David
作者单位：University of Illinois System; University of Illinois Urbana-Champaign; Harvard University; Amherst College
摘要：We consider the distribution of the Galois groups Gal(Kun/K)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\operatorname {Gal}(K<^>{\operatorname{un}}/K)$\end{document} of maximal unramified extensions as K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amss...
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作者：Stadler, Stephan
作者单位：Max Planck Society
摘要：This belongs to a series of papers motivated by Ballmann's Higher Rank Rigidity Conjecture. We prove the following. Let X be a CAT(0) space with a geometric group action Gamma curved right arrow X. Suppose that every geodesic in X lies in an n-flat, n >= 2. If X contains a periodic n-flat which does not bound a flat (n + 1)-half-space, then X is a Riemannian symmetric space, a Euclidean building or non-trivially splits as a metric product. This generalizes the Higher Rank Rigidity Theorem for ...
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作者：Chodosh, Otis; Daniels-Holgate, J. M.; Schulze, Felix
作者单位：Stanford University; Hebrew University of Jerusalem; University of Warwick
摘要：We prove Ilmanen's resolution of point singularities conjecture by establishing short-time smoothness of the level set flow of a smooth hypersurface with isolated conical singularities. This shows how the mean curvature flow evolves through asymptotically conical singularities. Precisely, we prove that the level set flow of a smooth hypersurface Mn subset of Rn+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy...
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作者：Drivas, Theodore D.; Elgindi, Tarek M.; Jeong, In-Jee
作者单位：State University of New York (SUNY) System; Stony Brook University; Duke University; Seoul National University (SNU); Seoul National University (SNU)
摘要：We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to establish a number of results that reveal a form of irreversibility in the Euler equations governing the motion of an incompressible and inviscid fluid. In particular, we show that nearby general stable steady states (i) all fluid flows exhibit indefinite twist...
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作者：Sawin, Will; Wood, Melanie Matchett
作者单位：Princeton University; Harvard University
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作者：Krah, Johannes
作者单位：University of Bielefeld
摘要：We construct a non-full exceptional collection of maximal length consisting of line bundles on the blow-up of the projective plane in 10 general points. As a consequence, the orthogonal complement of this collection is a universal phantom category. This provides a counterexample to a conjecture of Kuznetsov and to a conjecture of Orlov.
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作者：Chow, Sam; Yang, Lei
作者单位：University of Warwick; Institute for Advanced Study - USA
摘要：Given any line in the plane, we strengthen the Littlewood conjecture by two logarithms for almost every point on the line, thereby generalising the fibre result of Beresnevich, Haynes, and Velani. To achieve this, we prove an effective asymptotic equidistribution result for one-parameter unipotent orbits in SL(3, R)/SL(3, Z). We also provide a complementary convergence statement, by developing the structural theory of dual Bohr sets: at the cost of a slightly stronger Diophantine assumption, t...
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作者：Iyengar, Srikanth B.; Khare, Chandrashekhar B.; Manning, Jeffrey
作者单位：Utah System of Higher Education; University of Utah; University of California System; University of California Los Angeles
摘要：We define a congruence module Psi(A)(M) associated to a surjective O\-algebra morphism lambda:A -> O, with O a discrete valuation ring, A a complete noetherian local O-algebra regular at p, the kernel of lambda, and M a finitely generated A-module. We establish a numerical criterion for M to have a free direct summand over A of positive rank. It is in terms of the lengths of Psi(A)(M) and the torsion part of p/p(2). It generalizes results of Wiles, Lenstra, and Diamond, that deal with the case...
