Lossless Strichartz and spectral projection estimates on unbounded manifolds

Abstract

We prove new lossless Strichartz and spectral projection estimates on asymptotically hyperbolic surfaces, and, in particular, on all convex cocompact hyperbolic surfaces. In order to do this, we also obtain log-scale lossless Strichartz and spectral projection estimates on manifolds of uniformly bounded geometry with nonpositive and negative sectional curvatures, extending the recent works of the first two authors for compact manifolds. We are able to use these along with known $L^2$-local smoothing and new $L^2\to L^q$ half-localized resolvent estimates to obtain our lossless bounds.

Revised version to appear in GAFA, 81 pages. Corrections as well as new global results under natural conditions at the bottom of the spectrum