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作者：Marques, Fernando C.; Neves, Andre; Song, Antoine
作者单位：Princeton University; University of Chicago; Imperial College London
摘要：For almost all Riemannian metrics (in the C-infinity Baire sense) on a closed manifold Mn+1, 3 <= (n + 1) <= 7, we prove that there is a sequence of closed, smooth, embedded, connected minimal hypersurfaces that is equidistributed in M. This gives a quantitative version of the main result of Irie et al. (Ann Math 187(3): 963-972, 2018), that established density of minimal hypersurfaces for generic metrics. As in Irie et al. (2018), the main tool is the Weyl Law for the Volume Spectrum proven b...
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作者：Bartels, Arthur; Bestvina, Mladen
作者单位：University of Munster; Utah System of Higher Education; University of Utah
摘要：We prove the Farrell-Jones Conjecture for mapping class groups. The proof uses the Masur-Minsky theory of the large scale geometry of mapping class groups and the geometry of the thick part of Teichmuller space. The proof is presented in an axiomatic setup, extending the projection axioms in Bestvina et al. (Publ Math Inst Hautes Etudes Sci 122:1-64, 2015). More specifically, we prove that the action of on the Thurston compactification of Teichmuller space is finitely F-amenable for the family...
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作者：Ntalampekos, Dimitrios
作者单位：State University of New York (SUNY) System; Stony Brook University
摘要：We prove that the Sierpiski gasket is non-removable for quasiconformal maps, thus answering a question of Bishop (NSF Research Proposal, 2015. http://www.math.stonybrook.edu/similar to bishop/vita/nsf15.pdf). The proof involves a new technique of constructing an exceptional homeomorphism from R-2 into some non-planar surface S, and then embedding this surface quasisymmetrically back into the plane by using the celebrated Bonk-Kleiner Theorem (Bonk and Kleiner in Invent Math 150(1):127-183, 200...
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作者：Goldstein, Michael; Schlag, Wilhelm; Voda, Mircea
作者单位：University of Toronto; Yale University; University of Chicago
摘要：We study multi-frequency quasiperiodic Schrodinger operators on Z. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of a criterion for the spectrum to contain an interval at a given location that we establish non-perturbatively in the regime of positive Lyapunov exponent.
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作者：Antieau, Benjamin; Auel, Asher; Ingalls, Colin; Krashen, Daniel; Lieblich, Max
作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Yale University; Rutgers University System; Rutgers University New Brunswick; Rutgers University Newark; University of Washington; University of Washington Seattle
摘要：The standard period-index conjecture for Brauer groups of p-adic surfaces S predicts that ind(alpha) vertical bar per(alpha)3 for every alpha is an element of Br(Q(p)(S)). Using Gabber's theory of prime-to-l alterations and the deformation theory of twisted sheaves, we prove that ind(alpha) vertical bar per(alpha) 4 for alpha of period prime to 6p, giving the first uniform period-index bounds over such fields.
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作者：Kontsevich, Maxim; Tschinkel, Yuri
作者单位：Universite Paris Saclay; New York University; Simons Foundation
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作者：Wu, Sijue
作者单位：University of Michigan System; University of Michigan
摘要：We consider the two dimensional gravity water wave equation in a regime where the free interface is allowed to be non-C-1. In this regime, only a degenerate Taylor inequality -partial derivative P/partial derivative n >= 0 holds, with degeneracy at the singularities. In Kinsey and Wu (Camb J Math 6(2):93-181, 2018) an energy functional E(t) was constructed and an a-priori estimate was proved. The energy functional E(t) is not only finite for interfaces and velocities in Sobolev spaces, but als...
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作者：Kang, Seok-Jin; Kashiwara, Masaki; Kim, Myungho
作者单位：United Arab Emirates University; Kyoto University; Korea Institute for Advanced Study (KIAS); Kyung Hee University
摘要：We fix a mistake in [1] on the definition of commuting family of central objects.
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作者：Szymik, Markus; Wahl, Nathalie
作者单位：Norwegian University of Science & Technology (NTNU); University of Copenhagen
摘要：We prove that Thompson's group V is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman-Thompson groups V-n,V-r with the homology of the zeroth component of the infinite loop space of the mod n - 1 Moore spectrum. As V = V-2,V-1, we can deduce that this group is acyclic. Our proof involves establishing homological stability with respect to r, as well as a computation of the algebraic K-theory of the category of finitely generated ...
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作者：Eskin, Alex; Mirzakhani, Maryam; Rafi, Kasra
作者单位：University of Chicago; Stanford University; University of Toronto
摘要：We compute the asymptotic growth rate of the number N(C,R) of closed geodesics of length R in a connected component C of a stratum of quadratic differentials. We prove that, for any 01, the number of closed geodesics of length at most R such that spends at least -fraction of its time outside of a compact subset of C is exponentially smaller than N(C,R). The theorem follows from a lattice counting statement. For points x,y in the moduli space M(S) of Riemann surfaces, and for 01 we find an uppe...
