Lossless Strichartz and spectral projection estimates on unbounded manifolds

2025/04/09 by Xiaoqi Huang, Huang, Xiaoqi, Christopher D. Sogge +5 · 1 citation
Mathematics · Computer Science · #advanced mathematical theories #Topological and Geometric Data Analysis #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2504.07238

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 L²-local smoothing and new L² → L^q half-localized resolvent estimates to obtain our lossless bounds.

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• Spectral projection estimates restricted to uniformly embedded submanifolds

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