Resonances and scattering poles on asymptotically hyperbolic manifolds

2004/03/31 by Colin Guillarmou
Mathematics · #math.DG #math.FA #math.SP #msc:58J50 #msc:35P25

paper · pdf

published as Math. Res. Lett. 12 (2005), no. 1, 103--119. · 13 pages

arxiv created 2004/03/31 · arxiv updated 2009/12/01

Abstract

On an asymptotically hyperbolic manifold (X,g), we show that the resolvent resonances coincide, with multiplicities, with the poles of the renormalized scattering operator, except for the special points n/2-k (with k>0 integer) where an additional term appears: this is the dimension of the kernel of the k-conformal Laplacian on the boundary when (X,g) is Einstein.

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