Strichartz and Spectral Projection Estimates on Asymptotically Conic Manifolds

TL;DR

This paper establishes new Strichartz and spectral projection estimates on asymptotically conic and Euclidean manifolds, under curvature conditions near trapped sets, advancing understanding of wave behavior in geometric settings.

Contribution

It proves the lossless Strichartz theorem on asymptotically conic surfaces and spectral projection results on Euclidean-ended surfaces with curvature assumptions, extending prior spectral analysis.

Findings

Proved lossless Strichartz estimates on asymptotically conic surfaces with negative curvature near trapped sets.

Established spectral projection theorems on surfaces with Euclidean ends and nonpositive curvature.

Discussed spectral projection estimates on higher-dimensional asymptotically Euclidean manifolds with local smoothing conditions.

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.