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Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506—0027, USA, e-mail: perry@ms.uky.edu, , , , , , US

    P.A. Perry

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  1. P.A. Perry
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Submitted: March 2000.

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Perry, P. Asymptotics of the length spectrum for hyperbolic manifolds of infinite volume . GAFA, Geom. funct. anal. 11, 132–141 (2001). https://doi.org/10.1007/PL00001668

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  • DOI: https://doi.org/10.1007/PL00001668

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