Restriction estimates for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908488559493120 |
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| author | Li, Zhuoran Zheng, Jiqiang |
| author_facet | Li, Zhuoran Zheng, Jiqiang |
| contents | In this paper, we study the restriction problem for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$ with $n$ being odd. We obtain an $L^2-L^p$ restriction estimate, which is optimal except at the endpoint. Furthermore, we establish an $L^s-L^p$ restriction estimate for these hypersurfaces, which is achieved by improving the known $L^{\infty}$ restriction estimate for hypersurfaces with $\frac{n-1}{2}$ positive principal curvatures and $\frac{n-1}{2}$ negative principal curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Restriction estimates for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$ Li, Zhuoran Zheng, Jiqiang Analysis of PDEs In this paper, we study the restriction problem for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$ with $n$ being odd. We obtain an $L^2-L^p$ restriction estimate, which is optimal except at the endpoint. Furthermore, we establish an $L^s-L^p$ restriction estimate for these hypersurfaces, which is achieved by improving the known $L^{\infty}$ restriction estimate for hypersurfaces with $\frac{n-1}{2}$ positive principal curvatures and $\frac{n-1}{2}$ negative principal curvatures. |
| title | Restriction estimates for one class of hypersurfaces with vanishing curvature in $\mathbb{R}^n$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.08633 |