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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.02496 |
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| _version_ | 1866910430602985472 |
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| author | Moy, Julien |
| author_facet | Moy, Julien |
| contents | Let $(M,g)$ be a smooth connected Riemannian manifold. We show an improvement of flatness theorem for hypersurfaces of $M$ of bounded nonlocal mean curvature in the viscosity sense. It implies local $ C^{1,α}$ regularity of these hypersurfaces provided that they are sufficiently flat. It extends a result of Caffarelli, Roquejoffre and Savin in the Euclidean setting to the case of arbitrary Riemannian manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_02496 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $C^{1,α}$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds Moy, Julien Analysis of PDEs Let $(M,g)$ be a smooth connected Riemannian manifold. We show an improvement of flatness theorem for hypersurfaces of $M$ of bounded nonlocal mean curvature in the viscosity sense. It implies local $ C^{1,α}$ regularity of these hypersurfaces provided that they are sufficiently flat. It extends a result of Caffarelli, Roquejoffre and Savin in the Euclidean setting to the case of arbitrary Riemannian manifolds. |
| title | $C^{1,α}$ regularity of hypersurfaces of bounded nonlocal mean curvature in Riemannian manifolds |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.02496 |