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September 2015 A McShane-type identity for closed surfaces
Yi Huang
Nagoya Math. J. 219: 65-86 (September 2015). DOI: 10.1215/00277630-2887835


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.


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Yi Huang. "A McShane-type identity for closed surfaces." Nagoya Math. J. 219 65 - 86, September 2015.


Received: 11 October 2013; Accepted: 5 February 2014; Published: September 2015
First available in Project Euclid: 20 October 2015

zbMATH: 1332.57017
MathSciNet: MR3413573
Digital Object Identifier: 10.1215/00277630-2887835

Primary: 57M50
Secondary: 57N05

Keywords: geodesics , hyperbolic surfaces , McShane identities

Rights: Copyright © 2015 Editorial Board, Nagoya Mathematical Journal

Vol.219 • September 2015
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