# MathSciDoc: An Archive for Mathematician ∫

#### Geometric Analysis and Geometric Topologymathscidoc:1912.43782

arXiv preprint math/9801024, 1998.1
Given a compact orientable surface with finitely many punctures \Sigma , let \$\Cal S (\Sigma) \$ be the set of isotopy classes of essential unoriented simple closed curves in \Sigma . We determine a complete set of relations for a function from \$\Cal S (\Sigma) \$ to \$\bold R \$ to be the geodesic length function of a hyperbolic metric with geodesic boundary and cusp ends on \Sigma . As a conse quence, the Teichmller space of hyperbolic metrics with geodesic boundary and cusp ends on \Sigma is reconstructed from an intrinsic \$(\bold QP^ 1, PSL (2,\bold Z)) \$ structure on \$\Cal S (\Sigma) \$.
```@inproceedings{feng1998geodesic,