Главная

Jean-Marc Schlenker

  1. Maximal surfaces and the universal Teichm\"uller space.

    Втр, 11/24/2009 - 16:01 — SomNambul
    Authors: Jean-Marc Schlenker, Francesco Bonsante
    Subjects: Differential Geometry
    Abstract

    We show that any element of the universal Teichm\"uller space is realized by
    a unique minimal Lagrangian diffeomorphism from the hyperbolic plane to itself.
    The proof uses maximal surfaces in the 3-dimensional anti-de Sitter space. We
    show that, in $AdS^{n+1}$, any subset $E$ of the boundary at infinity which is
    the boundary at infinity of a space-like hypersurface bounds a maximal
    space-like hypersurface. In $AdS^3$, if $E$ is the graph of a quasi-symmetric
    homeomorphism, then this maximal surface is unique, and it has negative
    sectional curvature.

  2. On polynomial integrals over the orthogonal group.

    Чт, 10/08/2009 - 10:54 — SomNambul
    Authors: Jean-Marc Schlenker, Teodor Banica, Benoit Collins
    Subjects: Mathematical Physics
    Abstract

    We consider integrals of type $\int_{O_n}u_{11}^{a_1}...
    u_{1n}^{a_n}u_{21}^{b_1}... u_{2n}^{b_n} du$, with respect to the Haar measure
    on the orthogonal group. We establish several remarkable invariance properties
    satisfied by such integrals, by using combinatorial methods. We present as well
    a general formula for such integrals, as a sum of products of factorials.

  3. The convex core of quasifuchsian manifolds with particles.

    Чт, 09/24/2009 - 12:35 — SomNambul
    Authors: Jean-Marc Schlenker, Cyril Lecuire
    Subjects: Geometric Topology
    Abstract

    We consider quasifuchsian manifolds with "particles", i.e., cone
    singularities of fixed angle less than $\pi$ going from one connected component
    of the boundary at infinity to the other. Each connected component of the
    boundary at infinity is then endowed with a conformal structure marked by the
    endpoints of the particles. We prove that this defines a homeomorphism from the
    space of quasifuchsian metrics with $n$ particles (of fixed angle) and the
    product of two copies of the Teichm\"uller space of a surface with $n$ marked
    points.

  4. Volume maximization and the extended hyperbolic space.

    Пнд, 08/17/2009 - 18:30 — SomNambul
    Authors: Feng Luo, Jean-Marc Schlenker
    Subjects: Geometric Topology
    Abstract

    We consider a volume maximization program to construct hyperbolic structures
    on triangulated 3-manifolds, for which previous progress has lead to consider
    angle assignments which do not correspond to a hyperbolic metric on each
    simplex. We show that critical points of the generalized volume are associated
    to geometric structures modeled on the extended hyperbolic space -- the natural
    extension of hyperbolic space by the de Sitter space -- except for the
    degenerate case where all simplices are Euclidean in a generalized sense.

Math-arch

RSS-материал