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arXiv · 0712.3237

Local smoothing for scattering manifolds with hyperbolic trapped sets

Kiril Datchev
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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.

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Kiril Datchev. 2009-01-29. Local smoothing for scattering manifolds with hyperbolic trapped sets. https://doi.org/10.1007/s00220-008-0684-1

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