Lossless Strichartz and spectral projection estimates on unbounded manifolds
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911426266791936 |
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| author | Huang, Xiaoqi Sogge, Christopher D. Tao, Zhongkai Zhang, Zhexing |
| author_facet | Huang, Xiaoqi Sogge, Christopher D. Tao, Zhongkai Zhang, Zhexing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07238 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lossless Strichartz and spectral projection estimates on unbounded manifolds Huang, Xiaoqi Sogge, Christopher D. Tao, Zhongkai Zhang, Zhexing Analysis of PDEs Classical Analysis and ODEs Spectral Theory 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. |
| title | Lossless Strichartz and spectral projection estimates on unbounded manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Spectral Theory |
| url | https://arxiv.org/abs/2504.07238 |