Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912638636654592 |
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| author | Ji, Meng Kwong, Kwok-Kun |
| author_facet | Ji, Meng Kwong, Kwok-Kun |
| contents | In this paper, we uncover a novel connection between the Fenchel-Willmore inequality and a new logarithmic Sobolev inequality for mean-convex submanifolds immersed in non-negatively curved manifolds with Euclidean volume growth. Building on this connection, we establish extensions of the Fenchel-Willmore inequality to submanifolds with boundary and to complete non-compact submanifolds. In addition, we derive a sharp Sobolev-type inequality for submanifolds in the same setting. These Sobolev-type inequalities admit a number of applications, including topological consequences in the surface case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08053 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds Ji, Meng Kwong, Kwok-Kun Differential Geometry In this paper, we uncover a novel connection between the Fenchel-Willmore inequality and a new logarithmic Sobolev inequality for mean-convex submanifolds immersed in non-negatively curved manifolds with Euclidean volume growth. Building on this connection, we establish extensions of the Fenchel-Willmore inequality to submanifolds with boundary and to complete non-compact submanifolds. In addition, we derive a sharp Sobolev-type inequality for submanifolds in the same setting. These Sobolev-type inequalities admit a number of applications, including topological consequences in the surface case. |
| title | Fenchel-Willmore and Sobolev-type inequalities for submanifolds in non-negatively curved manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.08053 |