Strichartz estimates for the Schrödinger equation on Zoll manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915600998072320 |
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| author | Huang, Xiaoqi Sogge, Christopher D. |
| author_facet | Huang, Xiaoqi Sogge, Christopher D. |
| contents | We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ for solutions to the Schrödinger equation on Zoll manifolds, including, in particular, the standard round sphere $S^d$. The proof relies on the arithmetic properties of the spectrum of the Laplacian on Zoll manifolds, as well as bilinear oscillatory integral estimates, which allow us to relate the problem to Strichartz estimate on one-dimensional tori. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_00884 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for the Schrödinger equation on Zoll manifolds Huang, Xiaoqi Sogge, Christopher D. Analysis of PDEs Classical Analysis and ODEs Differential Geometry We obtain optimal space-time estimates in $L^q_{t,x}$ spaces for all $q\ge 2$ for solutions to the Schrödinger equation on Zoll manifolds, including, in particular, the standard round sphere $S^d$. The proof relies on the arithmetic properties of the spectrum of the Laplacian on Zoll manifolds, as well as bilinear oscillatory integral estimates, which allow us to relate the problem to Strichartz estimate on one-dimensional tori. |
| title | Strichartz estimates for the Schrödinger equation on Zoll manifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Differential Geometry |
| url | https://arxiv.org/abs/2505.00884 |