Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds
Spectral Theory
2009-11-11 v2 Analysis of PDEs
Abstract
We prove high energy estimates for the boundary values of the weighted resolvent of the Laplacian on an asymptotically hyperbolic manifold. Our point is to use weights that fit the pseudo-differential calculus associated with the asymptotically hyperbolic geometry. Our proof is a combination of a trick using Mourre theory and of results by Froese-Hislop and Cardoso-Vodev.
Keywords
Cite
@article{arxiv.math/0509622,
title = {Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds},
author = {Jean-Marc Bouclet},
journal= {arXiv preprint arXiv:math/0509622},
year = {2009}
}
Comments
Replaced with revised version of Tue, 27 September 2005. Typos corrected and proof of Proposition 4.3 changed