Geodesic
Geodesic length functions and Teichmüller spaces
Luo, Feng1
1 Department of Mathematics, Rutgers University, New Brunswick, NJ 08903
Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 34-41.

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S1079-6762-96-00008-X

Luo, Feng 1

1 Department of Mathematics, Rutgers University, New Brunswick, NJ 08903 
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Luo, Feng. Geodesic length functions and Teichmüller spaces. Electronic research announcements of the American Mathematical Society, Tome 02 (1996) no. 1, pp. 34-41. doi : 10.1090/S1079-6762-96-00008-X. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-96-00008-X/

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