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作者：Agostiniani, Virginia; Fogagnolo, Mattia; Mazzieri, Lorenzo
作者单位：University of Verona; University of Trento
摘要：In this paper we consider complete noncompact Riemannian manifolds (M, g) with nonnegative Ricci curvature and Euclidean volume growth, of dimension n >= 3. For every bounded open subset Omega subset of M with smooth boundary, we prove that integral(partial derivative Omega)vertical bar H/n-1 vertical bar(n-1) d sigma >= AVR(g)vertical bar Sn-1 vertical bar, where H is the mean curvature of partial derivative Omega and AVR(g) is the asymptotic volume ratio of (M, g). Moreover, the equality hol...
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作者：Mustata, Mircea; Popa, Mihnea
作者单位：University of Michigan System; University of Michigan; Northwestern University
摘要：We bound the generation level of the Hodge filtration on the localization along a hypersurface in terms of its minimal exponent. As a consequence, we obtain a local vanishing theorem for sheaves of forms with log poles. These results are extended to -divisors, and are derived from a result of independent interest on the generation level of the Hodge filtration on nearby and vanishing cycles.
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作者：Sah, Ashwin; Sawhney, Mehtaab; Stoner, David; Zhao, Yufei
作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Massachusetts Institute of Technology (MIT)
摘要：LetHbe a graph allowing loops as well as vertex and edge weights. We prove that, for every triangle-free graphGwithout isolated vertices, the weighted number of graph homomorphismshom(G,H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hom (G, H)$$\end{document}satisfies the inequalityhom(G,H)<=& x220f;uv is an el...
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作者：Hutchcroft, Tom; Pete, Gabor
作者单位：University of Cambridge; Budapest University of Technology & Economics
摘要：We prove that every countably infinite group with Kazhdan's property (T) has cost 1, answering a well-known question of Gaboriau. It remains open if they have fixed price 1.
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作者：Davila, Juan; del Pino, Manuel; Wei, Juncheng
作者单位：Universidad de Antioquia; Universidad de Chile; University of Bath; University of British Columbia
摘要：We construct finite time blow-up solutions to the 2-dimensional harmonic map flow into the sphere S-2, u(t) = Delta u + vertical bar del u vertical bar(2)u in Omega x (0, T) u = phi on partial derivative Omega x (0, T) u(., 0) = u(0) in Omega, where Omega is a bounded, smooth domain in R-2, u : Omega x (0, T) -> S-2, u(0) : (Omega) over bar -> S-2 is smooth, and phi = u(0)vertical bar(partial derivative Omega). Given any k points q(1), ..., q(k) in the domain, we find initial and boundary data...
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作者：Avila, Artur; Fayad, Bassam; Le Calvez, Patrice; Xu, Disheng; Zhang, Zhiyuan
作者单位：University of Zurich; Instituto Nacional de Matematica Pura e Aplicada (IMPA); Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Universite Paris Cite; Imperial College London; Institute for Advanced Study - USA
摘要：We prove that a Ck\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C<^>k$$\end{document}, k >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...
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作者：Andre, Y.; Corvaja, P.; Zannier, U.
作者单位：Sorbonne Universite; Universite Paris Cite; University of Udine; Scuola Normale Superiore di Pisa
摘要：Given a point. on a complex abelian variety A, its abelian logarithm can be expressed as a linear combination of the periods of A with real coefficients, the Betti coordinates of.. When ( A,.) varies in an algebraic family, these coordinates define a system of multivalued real-analytic functions. Computing its rank (in the sense of differential geometry) becomes important when one is interested about how often. takes a torsion value (for instance, Manin's theorem of the kernel implies that thi...
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作者：Bullett, Shaun; Lomonaco, Luna
作者单位：University of London; Queen Mary University London; Universidade de Sao Paulo
摘要：In 1994 S. Bullett and C. Penrose introduced the one complex parameter family of (2 : 2) holomorphic correspondences Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {F}_a$$\end{document} the correspondence Fa\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \us...
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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.
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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...
