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作者：Buzzi, Jerome; Crovisier, Sylvain; Sarig, Omri
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Weizmann Institute of Science
摘要：We study the entropy and Lyapunov exponents of invariant measures mu for smooth surface diffeomorphisms f, as functions of (f, mu). The main result is an inequality relating the discontinuities of these functions. One consequence is that for a C-infinity surface diffeomorphism, on any set of ergodic measures with entropy bounded away from zero, continuity of the entropy implies continuity of the exponents. Another consequence is the upper semicontinuity of the Hausdorff dimension on the set of...
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作者：Zhou, Yang
作者单位：Fudan University
摘要：In this paper, we prove a wall-crossing formula for epsilon-stable quasimaps to GIT quotients conjectured by Ciocan-Fontanine and Kim, for all targets in all genera, including the orbifold case. We prove that stability conditions in adjacent chambers give equivalent invariants, provided that both chambers are stable. In the case of genus-zero quasimaps with one marked point, we compute the invariants in the left-most stable chamber in terms of the small I-function. Using this we prove that the...
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作者：Liu, Ruochuan; Wang, Guozhen
作者单位：Peking University; Fudan University
摘要：A Correction to this paper has been published: 10.1007/s00222-022-01134-9
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作者：Calegari, Frank; Geraghty, David
作者单位：University of Chicago; Boston College
摘要：A Correction to this paper has been published: 10.1007/s00222-017-0749-x
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作者：Ko, Hyerim; Lee, Sanghyuk; Oh, Sewook
作者单位：Seoul National University (SNU)
摘要：Let M be the maximal operator associated to a smooth curve in R-3 which has nonvanishing curvature and torsion. We prove that M is bounded on L-p if and only if p > 3.
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作者：Bahouri, Hajer; Perelman, Galina
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Sorbonne Universite; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper is dedicated to the study of the derivative nonlinear Schrodinger equation on the real line. The local well-posedness of this equation in the Sobolev spaces H-s(R) is well understood since a couple of decades, while the global well-posedness is not completely settled. For the latter issue, the best known results up-to-date concern either Cauchy data in H-1/2(R) with mass strictly less than 4 pi or general initial conditions in the weighted Sobolev space H-2,H-2(R) . In this article,...
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作者：Bonnaillie-Noel, Virginie; Herau, Frederic; Raymond, Nicolas
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Nantes Universite; Universite d'Angers
摘要：The magnetic Schrodinger operator, with Neumann boundary condition, on a smooth, bounded, and simply connected domain Omega of the Euclidean plane is considered in the semiclassical limit. When Omega has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic...
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作者：Li, Chi
作者单位：Purdue University System; Purdue University; Rutgers University System; Rutgers University New Brunswick
摘要：Let X be any Q-Fano variety and Aut(X)(0) be the identity component of the automorphism group of X. Let G be a connected reductive subgroup of Aut(X)(0) that contains a maximal torus of Aut(X)(0). We prove that X admits a Kahler-Einstein metric if and only if X is G-uniformly K-stable. This proves a version of Yau-Tian-Donaldson conjecture for arbitrary singular Fano varieties. A key new ingredient is a valuative criterion for G-uniform K-stability.
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作者：Hausel, Tamas; Hitchin, Nigel
作者单位：Institute of Science & Technology - Austria; University of Oxford
摘要：We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. Themain ingredients are the Bialynicki-Birula theory of C*-actions on semiprojective varieties, C* characters of indices of C*-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier-Mukai transform along the Hitchin fibration, h...
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作者：Beentjes, Sjoerd Viktor; Calabrese, John; Rennemo, Jorgen Vold
作者单位：University of Edinburgh; Heriot Watt University; University of Edinburgh; University of Oslo
摘要：We prove the crepant resolution conjecture for Donaldson-Thomas invariants of hard Lefschetz 3-Calabi-Yau (CY3) orbifolds, formulated by Bryan-Cadman-Young, interpreting the statement as an equality of rational functions. In order to do so, we show that the generating series of stable pair invariants on any CY3 orbifold is the expansion of a rational function. As a corollary, we deduce a symmetry of this function induced by the derived dualising functor. Our methods also yield a proof of the o...
