On Teichmuller Space of Surface with Boundary

Details On Teichmuller Space of Surface with Boundary On Teichmuller Space of Surface with Boundary

2006-01-15

arxiv.org/abs/math/0601364v2

Mathematics

Geometric Topology

15 pages, minor changes, adding some remarks, to appear in Duke Mathematical Journal

Scientific paper

We characterization hyperbolic metrics on compact surfaces with boundary using a variational principle. As a consequence, a new parametrization of the Teichmuller space of compact surface with boundary is produced. In the new parametrization, the Teichmuller 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.

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