-
作者：Bartholdi, Laurent; Dudko, Dzmitry
作者单位：University of Gottingen; Universite PSL; Ecole Normale Superieure (ENS); State University of New York (SUNY) System; Stony Brook University
摘要：We considerThurston maps: branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuous deformation of maps along with their critical orbits) is decidable. More precisely, we consider the action of mapping class groups, by pre- and post-composition, on branched coverings, and encode them algebraically asmapping class bisets. We show how the mapping class biset of maps preserving a multicurve decomposes i...
-
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...
-
作者：Chang, Chieh-Yu; Mishiba, Yoshinori
作者单位：National Tsing Hua University; University of the Ryukyus
摘要：In the classical theory of multiple zeta values (MZV's), Furusho pro-posed a conjecture asserting that the p-adic MZV's satisfy the same Q-linear relations that their corresponding real-valued MZV counterparts satisfy. In this paper, we verify a stronger version of a function field analogue of Furusho's conjecture in the sense that we are able to deal with all linear relations over an algebraic closure of the given rational function field, not just the rational linear relations. To each tuple ...
-
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.
-
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...
-
作者：Budzinski, Thomas; Louf, Baptiste
作者单位：University of British Columbia; Universite Paris Cite
摘要：We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the planar stochastic hyperbolic triangulations (PSHT) defined in Curien (Probab Theory Relat Fields 165(3):509-540, 2016). The proof relies on a combinatorial argument and the Goulden-Jackson recurrence relation to obtain tightness, and probabilistic arguments showing the uniqueness of the limit. As a consequence, we obtain asympto...
-
作者：Meeks, William H., III; Mira, Pablo; Perez, Joaquin; Ros, Antonio
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Universidad Politecnica de Cartagena; University of Granada; University of Granada
摘要：We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.
-
作者：Kang, Moon-Jin; Vasseur, Alexis F.
作者单位：Korea Advanced Institute of Science & Technology (KAIST); University of Texas System; University of Texas Austin
摘要：We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier-Stokes systems. To take into account the vanishing viscosity limit, we show a contraction property for any large perturbations of viscous shocks to the Navier-Stokes system. The contraction estimate does not depend on the strength of the viscosity. This provides a good control on the inviscid limit process. We prove that, for any initial...
-
作者：Petersen, Peter; Wink, Matthias
作者单位：University of California System; University of California Los Angeles
摘要：We show that manifolds with [n/2]-positive curvature operators are rational homology spheres. This follows from a more general vanishing and estimation theorem for the pth Betti number of closed n-dimensional Riemannian manifolds with a lower bound on the average of the lowest n - p eigenvalues of the curvature operator. This generalizes results due to D. Meyer, Gallot-Meyer, and Gallot.
-
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.
