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Resolvent of the Laplacian on geometrically finite hyperbolic manifolds

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Abstract

For geometrically finite hyperbolic manifolds Γ\ℍn+1, we prove the meromorphic extension of the resolvent of Laplacian, Poincaré series, Einsenstein series and scattering operator to the whole complex plane. We also deduce the asymptotics of lattice points of Γ in large balls of ℍn+1 in terms of the Hausdorff dimension of the limit set of Γ.

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Authors and Affiliations

  1. DMA, U.M.R. 8553 CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, 75230, Paris cedex 05, France

    Colin Guillarmou

  2. Department of Mathematics, Stanford University, Stanford, CA, 94305, USA

    Rafe Mazzeo

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  1. Colin Guillarmou
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  2. Rafe Mazzeo
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Correspondence to Colin Guillarmou.

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Guillarmou, C., Mazzeo, R. Resolvent of the Laplacian on geometrically finite hyperbolic manifolds. Invent. math. 187, 99–144 (2012). https://doi.org/10.1007/s00222-011-0330-y

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  • DOI: https://doi.org/10.1007/s00222-011-0330-y

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