Mathematical Research Letters

Volume 16, Issue 4, July 2009 pp. 577-590.

Applications of Cutoff Resolvent Estimates to the Wave Equation

Authors: Hans Christianson
Author institution: Massachusetts Institute of Technology

Summary: We consider solutions to the linear wave equation on non-compact Riemannian manifolds without boundary when the geodesic flow admits a filamentary hyperbolic trapped set. We obtain a polynomial rate of local energy decay with exponent depending only on the dimension.

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