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Ren Guo

  1. Calculus of generalized hyperbolic tetrahedron.

    Втр, 07/06/2010 - 15:01 — SomNambul
    Authors: Ren Guo
    Subjects: Metric Geometry
    Abstract

    We calculate the Jacobian matrix of the dihedral angles of a generalized
    hyperbolic tetrahedron as functions of edge lengths and find the complete set
    of symmetries of this matrix.

  2. Cell decompositions of Teichm\"uller spaces of surfaces with boundary.

    Чт, 06/17/2010 - 15:01 — SomNambul
    Authors: Feng Luo, Ren Guo
    Subjects: Geometric Topology
    Abstract

    A family of coordinates $\psi_h$ for the Teichm\"uller space of a compact
    surface with boundary was introduced in \cite{l2}. In the work \cite{m1},
    Mondello showed that the coordinate $\psi_0$ can be used to produce a natural
    cell decomposition of the Teichm\"uller space invariant under the action of the
    mapping class group. In this paper, we show that the similar result also works
    for all other coordinate $\psi_h$ for any $h \geq 0$.

  3. Quasi-Fuchsian 3-Manifolds and Metrics on Teichm\"{u}ller Space.

    Втр, 09/15/2009 - 11:27 — SomNambul
    Authors: Ren Guo, Zheng Huang, Biao Wang
    Subjects: Differential Geometry
    Abstract

    An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an
    incompressible closed minimal surface with principal curvatures in the range of
    $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose
    locus in Teichm\"{u}ller space is represented as a path $\gamma$, we show that
    $\gamma$ joins the conformal structures of the two components of the conformal
    boundary of $M$.

  4. Quasi-Fuchsian 3-Manifolds and Metrics on Teichm\"{u}ller Space.

    Втр, 09/15/2009 - 11:27 — SomNambul
    Authors: Ren Guo, Zheng Huang, Biao Wang
    Subjects: Differential Geometry
    Abstract

    An almost Fuchsian 3-manifold is a quasi-Fuchsian manifold which contains an
    incompressible closed minimal surface with principal curvatures in the range of
    $(-1,1)$. Such a 3-manifold $M$ admits a foliation of parallel surfaces, whose
    locus in Teichm\"{u}ller space is represented as a path $\gamma$, we show that
    $\gamma$ joins the conformal structures of the two components of the conformal
    boundary of $M$.

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