Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909696108003328 |
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| author | Ji, Meng Kwong, Kwok-Kun |
| author_facet | Ji, Meng Kwong, Kwok-Kun |
| contents | We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenchel, Willmore, and others. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_07655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature Ji, Meng Kwong, Kwok-Kun Differential Geometry 53E10, 53A07, 53C42 We establish a sharp Fenchel-Willmore inequality for closed submanifolds of arbitrary dimension and codimension immersed in a complete Riemannian manifold with non-negative intermediate Ricci curvature and Euclidean volume growth. In the hypersurface case, this reduces to non-negative Ricci curvature. We also characterize the equality case. This generalizes the recent work of Agostiniani, Fogagnolo, and Mazzieri \cite{Agostiniani-Fogagnolo-Mazzieri}, as well as classical results by Chen, Fenchel, Willmore, and others. |
| title | Fenchel-Willmore inequality for submanifolds in manifolds with non-negative $k$-Ricci curvature |
| topic | Differential Geometry 53E10, 53A07, 53C42 |
| url | https://arxiv.org/abs/2507.07655 |