Strichartz and Spectral Projection Estimates on Asymptotically Conic Manifolds

Abstract

We prove the lossless unit interval Strichartz theorem on asymptotically conic surfaces, assuming that a large enough neighborhood of its trapped set has negative curvature. We also prove the spectral projection theorem on surfaces with Euclidean ends and nonpositive curvature, assuming a large enough neighborhood of its trapped set has negative curvature. We also discuss the spectral projection theorem on asymptotically Euclidean manifolds with dimension greater than or equal to 3, assuming some local smoothing estimates.