Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume

Authors
Perry, PA
Citation
Pa. Perry, Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume, GEO FUNCT A, 11(1), 2001, pp. 132-141
Citations number
23
Categorie Soggetti
Mathematics
Journal title
GEOMETRIC AND FUNCTIONAL ANALYSIS
ISSN journal
1016443X → ACNP
Volume
11
Issue
1
Year of publication
2001
Pages
132 - 141
Database
ISI
SICI code
1016-443X(2001)11:1<132:AOTLSF>2.0.ZU;2-E
Abstract
We compute the leading asymptotics of the counting function for closed geod esics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our re suit extends classical results of Selberg for compact and finite-volume surfaces to this class of infinite-volume hyperbolic manifolds.