On parameterizations of Teichmüller spaces of surfaces with boundary

Ren Guo Rutgers University

Differential Geometry mathscidoc:1609.10128

Journal of Differential Geometry, 82, (3), 629-640, 2009
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.
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@inproceedings{ren2009on,
  title={On parameterizations of Teichmüller spaces of surfaces with boundary},
  author={Ren Guo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911194022542868785},
  booktitle={Journal of Differential Geometry},
  volume={82},
  number={3},
  pages={629-640},
  year={2009},
}
Ren Guo. On parameterizations of Teichmüller spaces of surfaces with boundary. 2009. Vol. 82. In Journal of Differential Geometry. pp.629-640. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911194022542868785.
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