Improved local energy decay for the wave equation on asymptotically   Euclidean odd dimensional manifolds in the short range case
  We show improved local energy decay for the wave equation on asymptotically Euclidean manifolds in odd dimensions in the short range case. The precise decay rate depends on the decay of the metric towards the Euclidean metric. We also give estimates of powers of the resolvent of the wave propagator between weighted spaces. 
Jean-Francois Bony, Dietrich Hafner
math.AP math-ph math.MP