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作者：Barilari, Davide; Rizzi, Luca
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：We prove that ideal sub-Riemannian manifolds (i.e., admitting no non-trivial abnormal minimizers) support interpolation inequalities for optimal transport. A key role is played by sub-Riemannian Jacobi fields and distortion coefficients, whose properties are remarkably different with respect to the Riemannian case. As a byproduct, we characterize the cut locus as the set of points where the squared sub-Riemannian distance fails to be semiconvex, answering to a question raised by Figalli and Ri...
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作者：Becker, Simon; Han, Rui; Jitomirskaya, Svetlana
作者单位：University of Cambridge; University System of Georgia; Georgia Institute of Technology; University of California System; University of California Irvine
摘要：We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux phi/2 pi\documentclass through a honeycomb is irrational, the continuous spectrum is an unbounded Cantor set of Lebesgue measure zero.
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作者：Carrillo, J. A.; Hittmeir, S.; Volzone, B.; Yao, Y.
作者单位：Imperial College London; University of Vienna; Parthenope University Naples; University System of Georgia; Georgia Institute of Technology
摘要：We analyze under which conditions equilibration between two competing effects, repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction, occurs. This balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses. All stationary states with suitable regularity are shown to be radially symmetric by means of continuous Steiner symmetrization techniques. Calculus of variations tools allow us to show the existence of glo...
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作者：Li, Haozhao; Wang, Bing
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS; Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：We show that the mean curvature blows up at the first finite singular time for a closed smooth embedded mean curvature flow IN R-3
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作者：Naber, Aaron; Valtorta, Daniele
作者单位：Northwestern University; University of Zurich
摘要：Given a principal bundle PM over a Riemannian manifold with compact structure group G, let us consider a stationary Yang-Mills connection A with energy M|FA|2. If we consider a sequence of such connections Ai, then it is understood by Tian (Ann Math 151(1):193-268, 2000) that up to subsequence we can converge AiA to a singular limit connection such that the energy measures converge |FAi|2dvg|FA|2dvg+, where =e(x)dn-4 is the n-4 rectifiable defect measure. Our main result is to show, without ad...
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作者：Cai, Yuanqing; Friedberg, Solomon; Ginzburg, David; Kaplan, Eyal
作者单位：Boston College; Weizmann Institute of Science; Tel Aviv University; Bar Ilan University
摘要：We present an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and lo...
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作者：Eskenazis, Alexandros; Mendel, Manor; Naor, Assaf
作者单位：Princeton University; Open University Israel
摘要：We prove that not every metric space embeds coarsely into an Alexandrov space of nonpositive curvature. This answers a question ofGromov (Geometric group theory, Cambridge University Press, Cambridge, 1993) and is in contrast to the fact that any metric space embeds coarsely into an Alexandrov space of nonnegative curvature, as shown by Andoni et al. (Ann Sci Ec Norm Super (4) 51(3):657-700, 2018). We establish this statement by proving that a metric space which is q- barycentric for some q is...
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作者：Chung, Yong Moo; Rivera-Letelier, Juan; Takahasi, Hiroki
作者单位：Hiroshima University; University of Rochester; Keio University
摘要：We study the dynamics of smooth interval maps with non-flat critical points. For every such a map that is topologically exact, we establish the full (level-2) Large Deviation Principle for empirical means. In particular, the Large Deviation Principle holds for every non-renormalizable quadratic map. This includes the maps without physical measure found by Hofbauer and Keller, and challenges the widely-shared view of the Large Deviation Principle as a refinement of laws of large numbers.
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作者：Nguyen, Hop Dang; Trung, Ngo Viet
作者单位：Vietnam Academy of Science & Technology (VAST); Vietnam Academy of Science & Technology (VAST)
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作者：Schrader, Gus; Shapiro, Alexander
作者单位：Columbia University; University of Edinburgh
摘要：We construct an injective algebra homomorphism of the quantum group Uq(sln+1) into a quantum cluster algebra Ln associated to the moduli space of framed PGLn+1-local systems on a marked punctured disk. We obtain a description of the coproduct of Uq(sln+1) in terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of the R-matrix in terms of a mapping class group element corresponding to the half-Dehn twist rotating one puncture a...
