Resolvent of the Laplacian on geometrically finite hyperbolic manifolds

Colin Guillarmou; Rafe Mazzeo

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arXiv · 1002.2165

Resolvent of the Laplacian on geometrically finite hyperbolic manifolds

Colin Guillarmou·Rafe Mazzeo

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Abstract

For geometrically finite hyperbolic manifolds $Γ\backslash H^{n+1}$, 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 $H^{n+1}$ in terms of the Hausdorff dimension of the limit set of $Γ$.

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BibTeX RIS

Colin Guillarmou, Rafe Mazzeo. 2012-08-21. Resolvent of the Laplacian on geometrically finite hyperbolic manifolds. https://arxiv.org/abs/1002.2165

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