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作者：Colin, Vincent; Dehornoy, Pierre; Rechtman, Ana
作者单位：Nantes Universite; Ecole Centrale de Nantes; Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we obtain that on a closed 3-manifold, every nondegenerate Reeb vector field has either two or infinitely many periodic orbits, and two periodic orbits are possible only on the tight sphere or on a tight lens space. Moreover we get that if M is a closed oriented 3-manifold that is not a graph manifold, for example a hyperbolic manifold, then every nondegenerate Reeb vector...
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作者：Liu, Yi
作者单位：Peking University
摘要：For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups.
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作者：Greene, Joshua Evan; Lobb, Andrew
作者单位：Boston College; Durham University
摘要：For every smooth Jordan curve gamma and cyclic quadrilateral Q in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of Q to gamma. The proof relies on the theorem of Polterovich and Viterbo that an embedded Lagrangian torus in C-2 has minimum Maslov number 2.
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作者：Bamler, Richard H.
作者单位：University of California System; University of California Berkeley
摘要：We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, , 2020). Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence...
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作者：Solecki, Slawomir
作者单位：Cornell University
摘要：We show that, for a generic measure preserving transformation T, the closed group generated by T is not isomorphic to the topological group L-0(lambda, T) of all Lebesgue measurable functions from [0, 1] to T (taken with pointwise multiplication and the topology of convergence in measure). This result answers a question of Glasner and Weiss. The main step in the proof consists of showing that Koopman representations of ergodic boolean actions of L-0(lambda, T) possess a non-trivial spectral pr...
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作者：Tsuzuki, Nobuo
作者单位：Tohoku University
摘要：The minimal slope conjecture, which was proposed by K. S. Kedlaya, asserts that two irreducible overconvergent F-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are isomorphic to each other. We affirmatively solve the minimal slope conjecture for overconvergent F-isocrystals on curves and for overconvergent (Q) over bar (p)-F-isocrystals on smooth varieties over finite fields.
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作者：Eldan, Ronen; Gross, Renan
作者单位：Weizmann Institute of Science
摘要：We develop a new technique for proving concentration inequalities which relate the variance and influences of Boolean functions. Using this technique, we 1. Settle a conjecture of Talagrand (Combinatorica 17(2):275-285, 1997), proving that integral({-1,1}n) root h(f) (x)d mu(x) >= C . Var (f) . (log (1/Sigma Inf(i)(2)(f)))(1/2), where h(f) (x) is the number of edges at x along which f changes its value, mu(x) is the uniform measure on {-1, 1}(n), and Inf(i) (f) is the influence of the i-th coo...
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作者：Cheskidov, Alexey; Luo, Xiaoyutao
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Institute for Advanced Study - USA; Duke University
摘要：In this paper, we prove a sharp nonuniqueness result for the incompressible Navier-Stokes equations in the periodic setting. In any dimension d >= 2 and given any p < 2, we show the nonuniqueness of weak solutions in the class (LtL infinity)-L-p, which is sharp in view of the classical Ladyzhenskaya-Prodi-Serrin criteria. The proof is based on the construction of a class of non-Leray-Hopf weak solutions. More specifically, for any p < 2, q < infinity, and epsilon > 0, we construct non-Leray-Ho...
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作者：Eberhard, Sean; Jezernik, Urban
作者单位：University of Cambridge; University of Ljubljana
摘要：Let G = SCln(q) be a quasisimple classical group with n large, and let x(1),..., x(k) is an element of G be random, where k >= q(C). We show that the diameter of the resulting Cayley graph is bounded by q(2)n(O(1)) with probability 1 - o(1). In the particular case G = SLn(p) with p a prime of bounded size, we show that the same holds for k = 3.
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作者：Biquard, Olivier; Guenancia, Henri
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS)
摘要：Let X be a complex projectivemanifold and let D subset of X be a smooth divisor. In this article, we are interested in studying limits when ss -> 0 of Kahler-Einstein metrics omega(ss) with a cone singularity of angle 2 pi ss along D. In our first result, we assume that X \ D is a locally symmetric space and we show that omega(ss) converges to the locally symmetric metric and further give asymptotics of omega(ss) when X \ D is a ball quotient. Our second result deals with the case when X is Fa...
