## On Teichmüller spaces of surfaces with boundary

Venue: | MR 2350850 Zbl pre05196149 |

Citations: | 9 - 4 self |

### BibTeX

@INPROCEEDINGS{Luo_onteichmüller,

author = {Feng Luo},

title = {On Teichmüller spaces of surfaces with boundary},

booktitle = {MR 2350850 Zbl pre05196149},

year = {},

pages = {463--482}

}

### OpenURL

### Abstract

We characterize hyperbolic metrics on compact triangulated surfaces with boundary using a variational principle. As a consequence, a new parameterization of the Teichmüller space of compact surface with boundary is produced. In the new parameterization, the Teichmüller space becomes an open convex polytope. It is conjectured that the Weil-Petersson symplectic form can be expressed explicitly in terms of the new coordinate. 1.1. The purpose of this paper is to produce a new parameterization of the Teichmüller space of compact surface with non-empty boundary so that the lengths of the boundary components are fixed. In this new parameterization, the Teichmüller space becomes an explicit open convex polytope. Our result can be considered as the counter-part of