A McShane identity for closed surfaces

Details A McShane identity for closed surfaces A McShane identity for closed surfaces

2012-03-17

arxiv.org/abs/1203.3860v3

Mathematics

Differential Geometry

12 pages, 4 figures, results presented at the "Geometry and Arithmetic around Teichmueller Theory" at Galatasaray University i

Scientific paper

We prove a McShane identity - a series, expressed in terms of geodesic
lengths, that sums to \pi 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.

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