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作者：Maulik, Davesh; Toda, Yukinobu
作者单位：Massachusetts Institute of Technology (MIT); University of Tokyo
摘要：In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants are equivalent to other curve-counting theories such as Gromov-Witten theory and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces, our invariants agree with PT in...
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作者：Brotbek, Damian; Darondeau, Lionel
作者单位：Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; KU Leuven
摘要：Any smooth projective variety contains many complete intersection subvarieties with ample cotangent bundles, of each dimension up to half its own dimension.
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作者：Zhang, Hui-Chun; Zhu, Xi-Ping
作者单位：Sun Yat Sen University
摘要：In 1997, Jost (Calc Var PDE 5:1-19, 1997) and Lin (Collection of papers on geometry, analysis and mathematical physics, World Sci. Publ., River Edge, 1997), independently proved that every energy minimizing harmonic map from an Alexandrov space with curvature bounded from below to an Alexandrov space with non-positive curvature is locally Holder continuous. Lin (1997) proposed an open problem: can the Holder continuity be improved to Lipschitz continuity? J. Jost also asked a similar problem a...
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作者：Gui, Changfeng; Moradifam, Amir
作者单位：Hunan University; University of Texas System; University of Texas at San Antonio; University of California System; University of California Riverside
摘要：In this paper, we showthat the total area of two distinct surfaces with Gaussian curvature equal to 1, which are also conformal to the Euclidean unit disk with the same conformal factor on the boundary, must be at least 4p. In otherwords, the areas of these surfaces must cover the whole unit sphere after a proper rearrangement. We refer to this lower bound of total area as the Sphere Covering Inequality. The inequality and its generalizations are applied to a number of open problems related to...
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作者：Latala, Rafal; van Handel, Ramon; Youssef, Pierre
作者单位：University of Warsaw; Princeton University; Universite Paris Cite
摘要：Let X be a symmetric random matrix with independent but non-identically distributed centered Gaussian entries. We show that E parallel to X parallel to(Sp) asymptotic to E[(Sigma i(Sigma j Xij2)p/2)1/p] for any 2 <= p <= infinity, where Sp denotes the p-Schatten class and the constants are universal. The right-hand side admits an explicit expression in terms of the variances of thematrix entries. This settles, in the case p = infinity, a conjecture of the first author, and provides a complete ...
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作者：De Simoi, Jacopo; Liverani, Carlangelo
作者单位：University of Toronto; University of Rome Tor Vergata
摘要：We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and conclude with a completely new result (a local limit theorem) on the distribution of the process determined by the fluctuations around the average. The method of proof is based on a mixture of standard pairs and transfer operators that we expect to be applicable ...
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作者：Xie, Song-Yan
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：For the intersection family of general Fermat-type hypersurfaces in defined over an algebraically closed field , we extend Brotbek's symmetric differential forms by a geometric approach, and we further exhibit unveiled families of lower degree symmetric differential forms on all possible intersections of with coordinate hyperplanes. Thereafter, we develop what we call the 'moving coefficients method' to prove a conjecture made by Olivier Debarre: for a generic choice of hypersurfaces of degree...
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作者：Gouezel, Sebastien; Matheus, Frederic; Maucourant, Francois
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Nantes Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes
摘要：The fundamental inequality of Guivarc'h relates the entropy and the drift of random walks on groups. It is strict if and only if the random walk does not behave like the uniform measure on balls. We prove that, in any nonelementary hyperbolic group which is not virtually free, endowed with a word distance, the fundamental inequality is strict for symmetric measures with finite support, uniformly for measures with a given support. This answers a conjecture of S. Lalley. For admissible measures,...
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作者：Huang, Jingyin
作者单位：McGill University
摘要：Let G be a right-angled Artin group with defining graph and let H be a finitely generated group quasi-isometric to G. We show if G satisfies that (1) its outer automorphism group is finite; (2) does not contain any induced 4-cycles; (3) is star-rigid; then H is commensurable to G. We show condition (2) is sharp in the sense that if contains an induced 4-cycle, then there exists an H quasi-isometric to G but not commensurable to G. Moreover, one can drop condition (1) if H is a uniform lattice ...
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作者：Deroin, Bertrand; Kleptsyn, Victor; Navas, Andres
作者单位：CY Cergy Paris Universite; Centre National de la Recherche Scientifique (CNRS); CY Cergy Paris Universite; Universite de Rennes; Centre National de la Recherche Scientifique (CNRS); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rennes; Universidad de Santiago de Chile
摘要：We consider finitely generated groups of real-analytic circle diffeomorphisms. We show that if such a group admits an exceptional minimal set (i.e., a minimal invariant Cantor set), then its Lebesgue measure is zero; moreover, there are only finitely many orbits of connected components of its complement. For the case of minimal actions, we show that if the underlying group is (algebraically) free, then the action is ergodic with respect to the Lebesgue measure. This provides first answers to q...
