Sharp upper bounds on resonances for perturbations of hyperbolic space

Details Sharp upper bounds on resonances for perturbations of hyperbolic space Sharp upper bounds on resonances for perturbations of hyperbolic space

2009-10-13

arxiv.org/abs/0910.2439v2

Mathematics

Spectral Theory

35 pages, 9 figures. v2: minor corrections

Scientific paper

For certain compactly supported metric and/or potential perturbations of the Laplacian on $\mathbb{H}^{n+1}$, we establish an upper bound on the resonance counting function with an explicit constant that depends only on the dimension, the radius of the unperturbed region in $\mathbb{H}^{n+1}$, and the volume of the metric perturbation. This constant is shown to be sharp in the case of scattering by a spherical obstacle.

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