Local smoothing for scattering manifolds with hyperbolic trapped sets

Abstract

We prove a resolvent estimate for the Laplace-Beltrami operator on a scattering manifold with a hyperbolic trapped set, and as a corollary deduce local smoothing. We use a result of Nonnenmacher-Zworski to provide an estimate near the trapped region, a result of Burq and Cardoso-Vodev to provide an estimate near infinity, and the microlocal calculus on scattering manifolds to combine the two.

16 pages. Published version available at http://www.springerlink.com/content/r663321331243288/?p=5ad2fe4778a742e4949de2030a409358&pi=11

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