Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 219 (2015), 65-86.
A McShane-type identity for closed surfaces
We prove a McShane-type identity: a series, expressed in terms of geodesic lengths, that sums to 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.
Nagoya Math. J., Volume 219 (2015), 65-86.
Received: 11 October 2013
Accepted: 5 February 2014
First available in Project Euclid: 20 October 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 57N05: Topology of $E^2$ , 2-manifolds
Huang, Yi. A McShane-type identity for closed surfaces. Nagoya Math. J. 219 (2015), 65--86. doi:10.1215/00277630-2887835. https://projecteuclid.org/euclid.nmj/1445345517