Strichartz estimates for the wave equation on Riemannian manifolds of bounded curvature

Abstract

Wave packet methods have proven to be a useful tool for the study of dispersive effects of the wave equation with coefficients of limited differentiability. In this thesis, we use scaled wave packet methods to prove Strichartz estimates on compact Riemannian manifolds under the condition that the Riemannian curvature tensor is uniformly bounded. This improves upon prior results for the case of metrics with two bounded derivatives.