Sharp upper bounds on resonances for perturbations of hyperbolic space

Article type: Research Article

Authors: Borthwick, David

Affiliations: Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA. E-mail: davidb@mathcs.emory.edu

Abstract: For certain compactly supported metric and/or potential perturbations of the Laplacian on Hn+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 Hn+1, and the volume of the metric perturbation. This constant is shown to be sharp in the case of scattering by a spherical obstacle.

Keywords: resonances, scattering theory, hyperbolic space

DOI: 10.3233/ASY-2010-0995

Journal: Asymptotic Analysis, vol. 69, no. 1-2, pp. 45-85, 2010