Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds

Details Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds Resolvent estimates for the Laplacian on asymptotically hyperbolic manifolds

2005-09-27

arxiv.org/abs/math/0509622v2

Mathematics

Spectral Theory

Replaced with revised version of Tue, 27 September 2005. Typos corrected and proof of Proposition 4.3 changed

Scientific paper

10.1007/s00023-005-0259-z

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.

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