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Geodesic length functions and Teichm\" uller spaces

Feng Luo

Geometric Analysis and Geometric Topology mathscidoc: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) $.
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@inproceedings{feng1998geodesic,
  title={Geodesic length functions and Teichm\" uller spaces},
  author={Feng Luo},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205759383669346},
  booktitle={arXiv preprint math/9801024},
  year={1998},
}
Feng Luo. Geodesic length functions and Teichm\" uller spaces. 1998. In arXiv preprint math/9801024. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224205759383669346.
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