Mathematical Research Letters

Volume 16 (2009)

Number 4

Applications of Cutoff Resolvent Estimates to the Wave Equation

Pages: 577 – 590

DOI: http://dx.doi.org/10.4310/MRL.2009.v16.n4.a3

Author

Hans Christianson (Massachusetts Institute of Technology)

Abstract

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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