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作者：Bedrossian, Jacob; Blumenthal, Alex; Punshon-Smith, Sam
作者单位：University System of Maryland; University of Maryland College Park; University System of Georgia; Georgia Institute of Technology; Institute for Advanced Study - USA
摘要：We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov exponent of stochastic differential equations. Our method combines (i) a new identity connecting the top Lyapunov exponent to a Fisher information-like functional of the stationary density of the Markov process tracking tangent directions with (ii) a novel, quantitative version of Hormander's hypoelliptic regularity theory in an L-1 framework which estimates this (degenerate) Fisher information from below b...
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作者：Bowden, Jonathan; Gironella, Fabio; Moreno, Agustin
作者单位：University of Regensburg; Monash University; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Humboldt University of Berlin; University of Augsburg; Uppsala University; Institute for Advanced Study - USA
摘要：Given a contact structure on a manifold V together with a supporting open book decomposition, Bourgeois gave an explicit construction of a contact structure on V x T-2. We prove that all such structures are universally tight in dimension 5, independent of whether the original contact manifold is itself tight or overtwisted. In arbitrary dimensions, we provide obstructions to the existence of strong symplectic fillings of Bourgeois manifolds. This gives a broad class of new examples of weakly b...
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作者：Liu, Ruochuan; Wang, Guozhen
作者单位：Fudan University; Peking University
摘要：We introduce a new approach to determining the structure of topological cyclic homology by means of a descent spectral sequence. We carry out the computation for a p-adic local field with F-p-coefficients, including the case p = 2 which was only covered by motivic methods except in the totally unramified case.
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作者：Berti, Massimiliano; Maspero, Alberto; Ventura, Paolo
作者单位：International School for Advanced Studies (SISSA)
摘要：Small-amplitude, traveling, space periodic solutions -called Stokes waves- of the 2 dimensional gravity water waves equations in deep water are linearly unstable with respect to long-wave perturbations, as predicted by Benjamin and Feir in 1967. We completely describe the behavior of the four eigenvalues close to zero of the linearized equations at the Stokes wave, as the Floquet exponent is turned on. We prove in particular the conjecture that a pair of non-purely imaginary eigenvalues depict...
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作者：De Rosa, Antonio; Tione, Riccardo
作者单位：University System of Maryland; University of Maryland College Park; Max Planck Society
摘要：We prove that m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in L-p, p > m, are regular almost everywhere in every dimension and codimension. This provides partial or full answers to multiple open questions arising in the literature. The anisotropic energy is required to satisfy a novel ellipticity condition, which holds for instance in a C-1,C-1 neighborhood of the area functional. This condition is proved to imply the atomic condition. In particular we provide the fir...
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作者：Castella, Francesc; Grossi, Giada; Lee, Jaehoon; Skinner, Christopher
作者单位：University of California System; University of California Santa Barbara; Korea Advanced Institute of Science & Technology (KAIST); Princeton University
摘要：Let E/Q be an elliptic curve and p an odd prime where E has good reduction, and assume that E admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of E over an imaginary quadratic field in which p splits, which we relate to the anticyclotomic Iwasawa theory of characters by a variation of the method of Greenberg-Vatsal. As a result of our study we obtain proofs (under relatively mild hypotheses) of PerrinRiou's Heegner point main conjecture, a p-converse to the...
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作者：Xie, Junyi; Yuan, Xinyi
作者单位：Peking University
摘要：We give a proof of the full geometric Bogomolov conjecture.
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作者：Disegni, Daniel
作者单位：Ben-Gurion University of the Negev
摘要：Let G be the group (GL(2) x GU(1))/GL(1) over a totally real field F, and let X be a Hida family for G. Revisiting a construction of Howard and Fouquet, we construct an explicit section P of a sheaf of Selmer groups over X. We show, answering a question of Howard, that P is a universal Heegner class, in the sense that it interpolates geometrically defined Heegner classes at all the relevant classical points of X. We also propose a 'Bertolini-Darmon' conjecture for the leading term of P at clas...
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作者：Brue, Elia; Naber, Aaron; Semola, Daniele
作者单位：Institute for Advanced Study - USA; Northwestern University; University of Oxford
摘要：This paper studies the structure and stability of boundaries in noncollapsed RCD(K,N) spaces, that is, metric-measure spaces (X,d,H-N) with Ricci curvature bounded below. Our main structural result is that the boundary partial derivative X is homeomorphic to a manifold away from a set of codimension 2, and is N - 1 rectifiable. Along the way, we show effective measure bounds on the boundary and its tubular neighborhoods. These results are new even for Gromov-Hausdorff limits (M-i(N), d(gi), p(...
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作者：de Lizaur, Francisco Torres
作者单位：University of Toronto
摘要：We construct finite dimensional families of non-steady solutions to the Euler equations, existing for all time, and exhibiting all kinds of qualitative dynamics in the phase space, for example: strange attractors and chaos, invariant manifolds of arbitrary topology, and quasiperiodic invariant tori of any dimension. The main theorem of the paper, from which these families of solutions are obtained, states that for any given vector field X on a closed manifold N, there is a Riemannian manifold ...
