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作者：Ghazouani, Selim
作者单位：Universite Paris Saclay
摘要：In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator R acting on the space of C-3-generalised interval exchange transformations at fixed points (which are standard periodic type IETs). We show that R is hyperbolic and that the number of unstable direction is exactly that predicted by the ergodic theory of IETs and the work of Forni and Marmi-Moussa-Yoccoz. As a consequence w...
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作者：Meeks, William H., III; Tinaglia, Giuseppe
作者单位：University of Massachusetts System; University of Massachusetts Amherst; University of London; King's College London
摘要：We describe the lamination limits of sequences of compact disks M-n embedded in R-3 with constant mean curvature H-n, when the boundaries of these disks tend to infinity. This theorem generalizes to the non-zero constant mean curvature case Theorem 0.1 by Colding and Minicozzi (Ann Math 160:573-615, 2004) for minimal disks. We apply this theorem to prove the existence of a chord arc result for compact disks embedded in R-3 with constant mean curvature; this chord arc result generalizes Theorem...
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作者：Levinson, Jake; Purbhoo, Kevin
作者单位：Simon Fraser University; University of Waterloo
摘要：We prove a generalization of the Shapiro-Shapiro conjecture on Wronskians of polynomials, allowing the Wronskian to have complex conjugate roots. We decompose the real Schubert cell according to the number of real roots of the Wronski map, and define an orientation of each connected component. For each part of this decomposition, we prove that the topological degree of the restricted Wronski map is given as an evaluation of a symmetric group character. In the case where all roots are real, thi...
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作者：Kurinczuk, Robert; Skodlerack, Daniel; Stevens, Shaun
作者单位：Imperial College London; ShanghaiTech University; University of East Anglia
摘要：For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are conjugate. This completes work of the first and third authors who showed that every irreducible cuspidal C-representation of a classical group is compactly induced from a cuspidal type. We generalize Bushnell and Henniart's notion of endo-equivalence to sem...
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作者：Gekhtman, Ilya; Gerasimov, Victor; Potyagailo, Leonid; Yang, Wenyuan
作者单位：Technion Israel Institute of Technology; Universidade Federal de Minas Gerais; Universite de Lille; Peking University
摘要：For a random walk on a finitely generated group G we obtain a generalization of a classical inequality of Ancona. We deduce as a corollary that the identity map on G extends to a continuous equivariant surjection from the Martin boundary to the Floyd boundary, with preimages of conical points being singletons. This provides new results for Martin compactifications of relatively hyperbolic groups.
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作者：Ibarlucia, Tomas
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
摘要：We show that all groups of a distinguished class of large topological groups, that of Roelcke precompact Polish groups, have Kazhdan's Property (T). This answers a question of Tsankov and generalizes previous results by Bekka (for the infinite-dimensional unitary group) and by Evans and Tsankov (for oligomorphic groups). Further examples include the group Aut(mu) of measure-preserving transformations of the unit interval and the group Aut * (mu) of non-singular transformations of the unit inte...
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作者：Orponen, Tuomas
作者单位：University of Jyvaskyla
摘要：I prove that closed n-regular sets E subset of R-d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.
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作者：Hubner, Katharina; Schmidt, Alexander
作者单位：Hebrew University of Jerusalem; Ruprecht Karls University Heidelberg
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作者：Chen, Gao
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：In this paper, we prove that for any Kahler metrics omega(0) and chi on M, there exists a Kahler metric omega(phi) = omega(0) + root-1 partial derivative(partial derivative) over bar phi > 0 satisfying the J-equation tr omega(phi)chi = c if and only if (M, [omega(0)], [chi]) is uniformly J-stable. As a corollary, we find a sufficient condition for the existence of constant scalar curvature Kahler metrics with c(1) < 0. Using the same method, we also prove a similar result for the supercritical...
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作者：Lecouturier, Emmanuel
作者单位：Tsinghua University
摘要：Let N and p be primes such that p divides the numerator of N-1/12. In this paper, we study the rank g(p) of the completion of the Hecke algebra acting on cuspidal modular forms of weight 2 and level Gamma(0)(N) at the p-maximal Eisenstein ideal. We give in particular an explicit criterion to know if g(p) >= 3, thus answering partially a question of Mazur. In order to study g(p), we develop the theory of higher Eisenstein elements, and compute the first few such elements in four different Hecke...
