Resonances on some geometrically finite hyperbolic manifolds

Details Resonances on some geometrically finite hyperbolic manifolds Resonances on some geometrically finite hyperbolic manifolds

2004-12-02

arxiv.org/abs/math/0412064v1

Mathematics

Spectral Theory

18 pages, 3 figures

Scientific paper

We prove the meromorphic extension to C for the resolvent of the Laplacian on
a class of geometrically finite hyperbolic manifolds with infinite volume and
we give a polynomial bound on the number of resonances. This class notably
contains the geometrically finite quotients with rational non-maximal rank
cusps previously studied by Froese-Hislop-Perry.

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