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Electronic Research Announcements

ISSN 1079-6762



Geodesic length functions
and Teichmüller spaces

Author: Feng Luo
Journal: Electron. Res. Announc. Amer. Math. Soc. 2 (1996), 34-41
MSC (1991): Primary 32G15, 30F60
MathSciNet review: 1405967
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Abstract: Given a compact orientable surface $\Sigma $, let $\mathcal {S}(\Sigma )$ be the set of isotopy classes of essential simple closed curves in $\Sigma $. We determine a complete set of relations for a function from $\mathcal {S}(\Sigma )$ to $\mathbf {R}$ to be the geodesic length function of a hyperbolic metric with geodesic boundary on $\Sigma $. As a consequence, the Teichmüller space of hyperbolic metrics with geodesic boundary on $\Sigma $ is reconstructed from an intrinsic combinatorial structure on $\mathcal {S}(\Sigma )$. This also gives a complete description of the image of Thurston's embedding of the Teichmüller space.

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Additional Information

Feng Luo
Affiliation: Department of Mathematics, Rutgers University, New Brunswick, NJ 08903

Keywords: Hyperbolic metrics, geodesics, Teichm\"{u}ller spaces
Received by editor(s): April 9, 1996
Communicated by: Walter Neumann
Article copyright: © Copyright 1996 American Mathematical Society