Ren Guo
Calculus of generalized hyperbolic tetrahedron.
Tue, 07/06/2010 - 15:01 — SomNambulAuthors: Ren Guo
Subjects: Metric Geometry
AbstractWe 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.Cell decompositions of Teichm\"uller spaces of surfaces with boundary.
Thu, 06/17/2010 - 15:01 — SomNambulAuthors: Feng Luo, Ren Guo
Subjects: Geometric Topology
AbstractA 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 $h \geq 0$.Quasi-Fuchsian 3-Manifolds and Metrics on Teichm\"{u}ller Space.
Tue, 09/15/2009 - 11:27 — SomNambulAuthors: Ren Guo, Zheng Huang, Biao Wang
Subjects: Differential Geometry
AbstractAn 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 $M$.Quasi-Fuchsian 3-Manifolds and Metrics on Teichm\"{u}ller Space.
Tue, 09/15/2009 - 11:27 — SomNambulAuthors: Ren Guo, Zheng Huang, Biao Wang
Subjects: Differential Geometry
AbstractAn 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 $M$.
User login
