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作者：Lindenstrauss, E.; Mohammadi, A.
作者单位：Hebrew University of Jerusalem; University of California System; University of California San Diego
摘要：We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL2(R) in arithmetic quotients of SL2(C) and SL2(R) x SL2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.
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作者：Ionescu, Alexandru D.; Magyar, Akos; Mirek, Mariusz; Szarek, Tomasz Z.
作者单位：Princeton University; University System of Georgia; University of Georgia; Rutgers University System; Rutgers University New Brunswick; University of Wroclaw; Basque Center for Applied Mathematics (BCAM)
摘要：We establish pointwise almost everywhere convergence for ergodic averages along polynomial sequences in nilpotent groups of step two of measure-preserving transformations on sigma-finite measure spaces. We also establish corresponding maximal inequalities on Lp for 1 <=infinity and rho-variational inequalities on L2 for 2
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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：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...
