A quantitative approach to the regularity of a Riemannian surface
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908471129014272 |
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| author | Eilat, Matan |
| author_facet | Eilat, Matan |
| contents | We introduce two definitions with the purpose of quantifying the concept of a $C^{2,α}$ surface for $0 < α< 1$. The intrinsic definition is given in terms of the $α$-Hölder norm of the Gauss curvature function. The extrinsic one relies on the existence of a smooth local representation of the Riemannian metric. We show that these definitions are equivalent up to a constant depending on $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21921 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantitative approach to the regularity of a Riemannian surface Eilat, Matan Differential Geometry Metric Geometry We introduce two definitions with the purpose of quantifying the concept of a $C^{2,α}$ surface for $0 < α< 1$. The intrinsic definition is given in terms of the $α$-Hölder norm of the Gauss curvature function. The extrinsic one relies on the existence of a smooth local representation of the Riemannian metric. We show that these definitions are equivalent up to a constant depending on $α$. |
| title | A quantitative approach to the regularity of a Riemannian surface |
| topic | Differential Geometry Metric Geometry |
| url | https://arxiv.org/abs/2507.21921 |