Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/103324
Title: Generalizations of McShane's identity to hyperbolic cone-surfaces
Authors: Tan, S.P. 
Wong, Y.L. 
Zhang, Y.
Issue Date: Jan-2006
Citation: Tan, S.P.,Wong, Y.L.,Zhang, Y. (2006-01). Generalizations of McShane's identity to hyperbolic cone-surfaces. Journal of Differential Geometry 72 (1) : 73-112. ScholarBank@NUS Repository.
Abstract: We generalize McShane's identity for the length series of simple closed geodesics on a cusped hyperbolic surface [19] to a general identity for hyperbolic cone-surfaces (with all cone angles ≤ π), possibly with cusps and/or geodesic boundary. The general identity is obtained by studying gaps formed by simple-normal geodesies emanating from a distinguished cone point, cusp or boundary geodesic. In particular, by applying the generalized identity to the quotient orbifolds of a hyperbolic one-cone/one-hole torus by its elliptic involution and of a hyperbolic closed genus two surface by its hyperelliptic involution, we obtain general Weierstrass identities for the one-cone/one-hole torus, and an identity for the genus two surface, which are also obtained by McShane using different methods in [20], [22] and [21]. We also give an interpretation of the general identity in terms of complex lengths of the cone points, cusps and geodesic boundary components.
Source Title: Journal of Differential Geometry
URI: http://scholarbank.nus.edu.sg/handle/10635/103324
ISSN: 0022040X
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

Page view(s)

32
checked on Oct 5, 2018

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.