A McShane-type Identity for Closed Surfaces

Yi Huang Tsinghua University

Differential Geometry Geometric Analysis and Geometric Topology arXiv subject: Geometric Topology (math.GT) arXiv subject: Differential Geometry (math.DG) mathscidoc:2206.10002

Nagoya Mathematical Journal, 219, 65, 2015.9
We prove a McShane-type identity: a series, expressed in terms of geodesic lengths, that sums to 2π for any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.
hyperbolic surfaces, McShane identity, geodesics
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@inproceedings{yi2015a,
  title={A McShane-type Identity for Closed Surfaces},
  author={Yi Huang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608151041132162342},
  booktitle={Nagoya Mathematical Journal},
  volume={219},
  pages={65},
  year={2015},
}
Yi Huang. A McShane-type Identity for Closed Surfaces. 2015. Vol. 219. In Nagoya Mathematical Journal. pp.65. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220608151041132162342.
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