Resonances on some geometrically finite hyperbolic manifolds

2004/12/02 by Colin Guillarmou, Guillarmou, Colin
Mathematics · #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP #msc:58J50

paper · pdf · doi:10.48550/arxiv.math/0412064

18 pages, 3 figures

arxiv created 2004/12/02 · arxiv updated 2009/12/01

Abstract

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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