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arXiv · 2504.07238

Lossless Strichartz and spectral projection estimates on unbounded manifolds

Xiaoqi Huang·Christopher D. Sogge·Zhongkai Tao·Zhexing Zhang
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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.

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Xiaoqi Huang, Christopher D. Sogge, Zhongkai Tao, Zhexing Zhang. 2025-04-09. Lossless Strichartz and spectral projection estimates on unbounded manifolds. https://arxiv.org/abs/2504.07238

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