Strichartz Estimates for Schrödinger Equations on Scattering Manifolds

Abstract

The present article is concerned with Schrödinger equations on non-compact Riemannian manifolds with asymptotically conic ends. It is shown that, for any admissible pair (including the endpoint), local in time Strichartz estimates outside a large compact set are centered at origin hold. Moreover, we prove global in space Strichartz estimates under the nontrapping condition on the metric.