%0 Journal Article
%T On parameterizations of Teichm¨šller spaces of surfaces with boundary
%A Ren Guo
%J Mathematics
%D 2006
%I arXiv
%X In \cite{rigidity}, Luo introduced a $\psi_{\lambda}$ edge invariant which turns out to be a coordinate of the Teichm\"uller space of a surface with boundary. And he proved that for $\lambda \geq 0$, the image of the Teichm\"uller space under $\psi_{\lambda}$ edge invariant coordinate is an open cell. In this paper we verify his conjecture that for $\lambda<0$, the image of the Teichm\"uller space is a bounded convex polytope.
%U http://arxiv.org/abs/math/0612221v1