On teichmüller spaces of surfaces with boundary

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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 a compact surface with boundary is produced. In the new parameterization, the Teichmüller space becomes an explicit open convex polytope. Our results can be considered as a generalization of the simplicial coordinate of Penner [P1], [P2] for hyperbolic metrics with cusp ends to the case of surfaces with geodesic boundary. It is conjectured that the Weil-Petersson symplectic form can be expressed explicitly in terms of the new coordinate.

Original languageEnglish (US)
Pages (from-to)463-482
Number of pages20
JournalDuke Mathematical Journal
Volume139
Issue number3
DOIs
StatePublished - Sep 15 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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