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作者：Jabin, Pierre-Emmanuel; Wang, Zhenfu
作者单位：University System of Maryland; University of Maryland College Park; University System of Maryland; University of Maryland College Park; University of Pennsylvania
摘要：We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space W--1,W-infinity thus including the Biot-Savart law and the point ...
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作者：Linowitz, Benjamin; McReynolds, D. B.; Pollack, Paul; Thompson, Lola
作者单位：University System of Ohio; Oberlin College; Purdue University System; Purdue University; University System of Georgia; University of Georgia
摘要：The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manif...
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作者：Lenzmann, Enno; Schikorra, Armin
作者单位：University of Basel; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：We consider the energy-critical half-wave maps equation . We give a complete classification of all traveling solitary waves with finite energy. The proof is based on a geometric characterization of these solutions as minimal surfaces with (not necessarily free) boundary on . In particular, we discover an explicit Lorentz boost symmetry, which is implemented by the conformal Mobius group on the target applied to half-harmonic maps from to . Complementing our classification result, we carry out ...
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作者：Jaffard, Stephane; Martin, Bruno
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Gustave-Eiffel; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite du Littoral-Cote-d'Opale
摘要：The Brjuno function B is a 1-periodic, nowhere locally bounded function, introduced by Yoccoz because it encapsulates a key information concerning analytic small divisor problems in dimension 1. We show that regularity, introduced by Caldern and Zygmund, is the only one which is relevant in order to unfold the pointwise regularity properties of B; we determine its regularity at every point and show that it is directly related to the irrationality exponent : its p-exponent at x is exactly . Thi...
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作者：Cieliebak, K.; Mohnke, K.
作者单位：University of Augsburg; Humboldt University of Berlin
摘要：We use a neck stretching argument for holomorphic curves to produce symplectic disks of small area and Maslov class with boundary on Lagrangian submanifolds of nonpositive curvature. Applications include the proof of Audin's conjecture on the Maslov class of Lagrangian tori in linear symplectic space, the construction of a new symplectic capacity, obstructions to Lagrangian embeddings into uniruled symplectic manifolds, a quantitative version of Arnold's chord conjecture, and estimates on the ...
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作者：Balla, Igor; Draxler, Felix; Keevash, Peter; Sudakov, Benny
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Oxford
摘要：A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R-n was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle theta and sufficiently large there are at most 2n-2 lines in R-n with common angle theta. Moreover, this bound is achieved if and only if theta = a...
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作者：Mirek, Mariusz; Stein, Elias M.; Trojan, Bartosz
作者单位：Institute for Advanced Study - USA; University of Wroclaw; Princeton University; Wroclaw University of Science & Technology
摘要：We prove l(p)(Z(d)) bounds for p is an element of(1,infinity) of r-variations r is an element of(2,infinity) for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.
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作者：Blumenthal, Alex; Young, Lai-Sang
作者单位：New York University
摘要：We consider C-2 Frechet differentiable mappings of Banach spaces leaving invariant compactly supported Borel probability measures, and study the relation between entropy and volume growth for a natural notion of volume defined on finite dimensional subspaces. SRB measures are characterized as exactly those measures for which entropy is equal to volume growth on unstable manifolds, equivalently the sum of positive Lyapunov exponents of the map. In addition to numerous difficulties incurred by o...
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作者：Guo, Yan; Kim, Chanwoo; Tonon, Daniela; Trescases, Ariane
作者单位：Brown University; University of Wisconsin System; University of Wisconsin Madison; Centre National de la Recherche Scientifique (CNRS); Universite PSL; Universite Paris-Dauphine; Universite Paris Saclay
摘要：A basic question about regularity of Boltzmann solutions in the presence of physical boundary conditions has been open due to characteristic nature of the boundary as well as the non-local mixing of the collision operator. Consider the Boltzmann equation in a strictly convex domain with the specular, bounce-back and diffuse boundary condition. With the aid of a distance function toward the grazing set, we construct weighted classical solutions away from the grazing set for all boundary conditi...
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作者：Fresan, Javier
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：At the end of the 1970s, Gross and Deligne conjectured that periods of geometric Hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments, with exponents determined by the Hodge decomposition. We prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order, thus improving previous results of Maillot and Rossler. The proof relies on a product formula for per...
