Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929234159599616 |
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| author | Jin, Xiaoshang Yin, Jiabin |
| author_facet | Jin, Xiaoshang Yin, Jiabin |
| contents | In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with ${\rm Ric}\geq-ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to the Riemannian manifold of negative curvature. As an application, we construct a Willmore-type inequality for closed hypersurfaces in hyperbolic space and obtain the characterization of geodesic sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below Jin, Xiaoshang Yin, Jiabin Differential Geometry In this paper, we establish a Willmore-type inequality for closed hypersurfaces in a complete Riemannian manifold of dimension $n+1$ with ${\rm Ric}\geq-ng$. It extends the classic result of Argostianiani, Fogagnolo, and Mazzieri in [1] to the Riemannian manifold of negative curvature. As an application, we construct a Willmore-type inequality for closed hypersurfaces in hyperbolic space and obtain the characterization of geodesic sphere. |
| title | Willmore-type inequality for closed hypersurfaces in complete manifolds with Ricci curvature bounded below |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.02465 |