Mathematical Research Letters

Volume 16 (2009)

Number 4

Applications of Cutoff Resolvent Estimates to the Wave Equation

Pages: 577 – 590



Hans Christianson (Massachusetts Institute of Technology)


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.

Published 1 January 2009