Resolvent Estimates for the Laplacian on Asymptotically Hyperbolic Manifolds
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.
- Publication:
-
Annales Henri Poincaré
- Pub Date:
- April 2006
- DOI:
- 10.1007/s00023-005-0259-z
- arXiv:
- arXiv:math/0509622
- Bibcode:
- 2006AnHP....7..527B
- Keywords:
-
- Spectral Theory;
- Analysis of PDEs
- E-Print:
- Replaced with revised version of Tue, 27 September 2005. Typos corrected and proof of Proposition 4.3 changed