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作者：Colding, Tobias Holck; Minicozzi, William P., II
作者单位：Massachusetts Institute of Technology (MIT)
摘要：A mean curvature flow starting from a closed embedded hyper-surface in Rn+1 must develop singularities. We show that if the flow has only generic singularities, then the space-time singular set is contained in finitely many compact embedded (n - 1)-dimensional Lipschitz submanifolds plus a set of dimension at most n-2. If the initial hypersurface is mean convex, then all singularities are generic and the results apply. In R-3 and R-4, we show that for almost all times the evolving hypersurface...
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作者：Bayer, Arend; Macri, Emanuele; Stellari, Paolo
作者单位：University of Edinburgh; University of Edinburgh; Heriot Watt University; University System of Ohio; Ohio State University; Northeastern University; University of Milan
摘要：We describe a connected component of the space of stability conditions on abelian threefolds, and on Calabi-Yau threefolds obtained as (the crepant resolution of) a finite quotient of an abelian threefold. Our proof includes the following essential steps:We simultaneously strengthen a conjecture by the first two authors and Toda, and prove that it follows from a more natural and seemingly weaker statement. This conjecture is a Bogomolov-Gieseker type inequality involving the third Chern charac...
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作者：Dolbeault, Jean; Esteban, Maria J.; Loss, Michael
作者单位：Universite PSL; Universite Paris-Dauphine; University System of Georgia; Georgia Institute of Technology
摘要：This paper is motivated by the characterization of the optimal symmetry breaking region in Caffarelli-Kohn-Nirenberg inequalities. As a consequence, optimal functions and sharp constants are computed in the symmetry region. The result solves a longstanding conjecture on the optimal symmetry range. As a byproduct of our method we obtain sharp estimates for the principal eigenvalue of Schrodinger operators on some non-flat non-compact manifolds, which to the best of our knowledge are new. The me...
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作者：Patrikis, Stefan
作者单位：Utah System of Higher Education; University of Utah
摘要：For any simple algebraic group G of exceptional type, we construct geometric -adic Galois representations with algebraic monodromy group equal to G, in particular producing the first such examples in types and . To do this, we extend to general reductive groups Ravi Ramakrishna's techniques for lifting odd two-dimensional Galois representations to geometric -adic representations.
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作者：Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite
摘要：We provide a rigorous derivation of the Brownian motion as the limit of a deterministic system of hard-spheres as the number of particles goes to infinity and their diameter simultaneously goes to , in the fast relaxation limit (with a suitable diffusive scaling of the observation time). As suggested by Hilbert in his sixth problem, we rely on a kinetic formulation as an intermediate level of description between the microscopic and the fluid descriptions: we use indeed the linear Boltzmann equ...
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作者：Danciger, Jeffrey; Gueritaud, Francois; Kassel, Fanny
作者单位：University of Texas System; University of Texas Austin; Centre National de la Recherche Scientifique (CNRS); Universite de Lille
摘要：We study strip deformations of convex cocompact hyperbolic surfaces, defined by inserting hyperbolic strips along a collection of disjoint geodesic arcs properly embedded in the surface. We prove that any deformation of the surface that uniformly lengthens all closed geodesics can be realized as a strip deformation, in an essentially unique way. The infinitesimal version of this result gives a parameterization, by the arc complex, of the moduli space of Margulis spacetimes with fixed convex co...
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作者：Astala, K.; Gonzalez, M. J.
作者单位：University of Helsinki; Universidad de Cadiz
摘要：We study the relation between the geometric properties of a quasicircle and the complex dilatation of a quasiconformal mapping that maps the real line onto . Denoting by S the Beurling transform, we characterize Bishop-Jones quasicircles in terms of the boundedness of the operator on a particular weighted space, and chord-arc curves in terms of its invertibility. As an application we recover the boundedness of the Cauchy integral on chord-arc curves.
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作者：Buhovsky, Lev; Opshtein, Emmanuel
作者单位：Tel Aviv University; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS)
摘要：This paper proceeds with the study of the -symplectic geometry of smooth submanifolds, as initiated in HumiliSre et al. (Duke Math J 164(4), 767-799, 2015) and Opshtein (Ann Sci A parts per thousand c Norm Sup,r 42(5), 857-864, 2009), with the main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension 4 symplectic submanifolds (-flexibility), while this is...
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作者：Rouquier, Raphael; Shan, Peng; Varagnolo, Michela; Vasserot, Eric
作者单位：University of California System; University of California Los Angeles; Universite Paris Saclay; CY Cergy Paris Universite; Universite Paris Cite
摘要：Varagnolo and Vasserot conjectured an equivalence between the category for CRDAHA's and a subcategory of an affine parabolic category O of type A. We prove this conjecture. As applications, we prove a conjecture of Rouquier on the dimension of simple modules of CRDAHA's and a conjecture of Chuang-Miyachi on the Koszul duality for the category of CRDAHA's.
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作者：Eynard-Bontemps, Helene
作者单位：Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We study the topology of the space of smooth codimension one foliations on a closed 3-manifold. We regard this space as the space of integrable plane fields included in the space of all smooth plane fields. It has been known since the late 60's that every plane field can be deformed continuously to an integrable one, so the above inclusion induces a surjective map between connected components. We prove that this map is actually a bijection.
