Resonances and scattering poles on asymptotically hyperbolic manifolds

Mathematics – Differential Geometry

Scientific paper

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13 pages

Scientific paper

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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