Reilly inequality for Varifolds
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908445945364480 |
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| author | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy |
| author_facet | Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy |
| contents | The famous Reilly inequality gives an upper bound for the first eigenvalue of the Laplacian defined on compact submanifolds of the Euclidean space in terms of the $L^2$-norm of the mean curvature vector. In this paper, we generalize this inequality in a Varifold context. In particular we generalize it for the class of $H(2)$ varifolds and for polygons and we analyse the equality case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_08354 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reilly inequality for Varifolds Grosjean, Jean-François Lemenant, Antoine Mougenot, Rémy Differential Geometry The famous Reilly inequality gives an upper bound for the first eigenvalue of the Laplacian defined on compact submanifolds of the Euclidean space in terms of the $L^2$-norm of the mean curvature vector. In this paper, we generalize this inequality in a Varifold context. In particular we generalize it for the class of $H(2)$ varifolds and for polygons and we analyse the equality case. |
| title | Reilly inequality for Varifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.08354 |