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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.05225 |
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| _version_ | 1866916315453718528 |
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| author | Kemp, Dóminique |
| author_facet | Kemp, Dóminique |
| contents | We extend previous work on the two-dimensional developable tangent surface to its higher dimensional analogues $\mathfrak{M} \subset \mathbb{R}^{n+1}$. The approach here similarly applies cylindrical approximate decoupling at its core, albeit in a new format. However, the presence of additional rulings as $n$ increases necessitates a case-by-case analysis, which in itself reveals interesting aspects of the geometry of $\mathfrak{M}$. The contributions of this paper can be viewed as culminating in the optimal $\ell^2(L^p)$ decoupling over Frenet boxes approximating a suitably defined, arbitrarily thin neighborhood of a curve $ϕ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05225 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoupling for Ruled Hypersurfaces Generated by a Curve Kemp, Dóminique Classical Analysis and ODEs We extend previous work on the two-dimensional developable tangent surface to its higher dimensional analogues $\mathfrak{M} \subset \mathbb{R}^{n+1}$. The approach here similarly applies cylindrical approximate decoupling at its core, albeit in a new format. However, the presence of additional rulings as $n$ increases necessitates a case-by-case analysis, which in itself reveals interesting aspects of the geometry of $\mathfrak{M}$. The contributions of this paper can be viewed as culminating in the optimal $\ell^2(L^p)$ decoupling over Frenet boxes approximating a suitably defined, arbitrarily thin neighborhood of a curve $ϕ$. |
| title | Decoupling for Ruled Hypersurfaces Generated by a Curve |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2407.05225 |