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arXiv · 1203.3860

A McShane-type identity for closed surfaces

Yi Huang
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Abstract

We prove a McShane-type identity - a series, expressed in terms of geodesic lengths, that sums to 2πfor 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.

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Yi Huang. 2012-09-28. A McShane-type identity for closed surfaces. https://arxiv.org/abs/1203.3860

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