Sharp upper bounds on resonances for perturbations of hyperbolic space

• Type of Material: Article
• Authors: David Borthwick, Emory University
• Language: English
• Date: 2010
• Publisher: IOS Press
• Publication Version: Preprint (Prior to Peer Review)
• Copyright Statement: © 2010 – IOS Press
• Final Published Version (URL): http://dx.doi.org/10.3233/ASY-2010-0995
• Title of Journal or Parent Work: Asymptotic Analysis
• ISSN: 0921-7134
• Volume: 69
• Issue: 1
• Start Page: 45
• End Page: 85
• Grant/Funding Information: Supported in part by NSF Grant DMS-09-01937.
• Research Categories: Mathematics

Abstract

For certain compactly supported metric and/or potential perturbations of the Laplacian on 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 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.