Spectral analysis of the Laplacian on geometrically finite hyperbolic manifolds
Résumé
For geometrically finite hyperbolic manifolds $\Gamma\backslash H^{n+1}$, 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 $\Gamma$ in large balls of $H^{n+1}$ in terms of the Hausdorff dimension of the limit set of $\Gamma$.
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