Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume

Peter A. Perry

doi:10.1007/PL00001668

Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume

Peter A. Perry

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and finite-volume surfaces to this class of infinite-volume hyperbolic manifolds.

Original language	English
Pages (from-to)	132-141
Number of pages	10
Journal	Geometric and Functional Analysis
Volume	11
Issue number	1
DOIs	https://doi.org/10.1007/PL00001668
State	Published - 2001

Bibliographical note

Funding Information:
Supported in part by NSF grant DMS-9707051.

Funding

Supported in part by NSF grant DMS-9707051.

Funders	Funder number
National Science Foundation (NSF)	DMS-9707051

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/PL00001668

Cite this

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title = "Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume",

abstract = "We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and finite-volume surfaces to this class of infinite-volume hyperbolic manifolds.",

author = "Perry, {Peter A.}",

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AU - Perry, Peter A.

N1 - Funding Information: Supported in part by NSF grant DMS-9707051.

PY - 2001

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N2 - We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and finite-volume surfaces to this class of infinite-volume hyperbolic manifolds.

AB - We compute the leading asymptotics of the counting function for closed geodesics on a convex co-compact hyperbolic manifold in terms of spectral data and scattering resonances for the Laplacian. Our result extends classical results of Selberg for compact and finite-volume surfaces to this class of infinite-volume hyperbolic manifolds.

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U2 - 10.1007/PL00001668

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 1

ER -

Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume

Abstract

Bibliographical note

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ASJC Scopus subject areas

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