Wulff inequality for minimal submanifolds in Euclidean space
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912170231463936 |
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| author | Du, Wenkui Yi, Yuchao Zhao, Ziyi |
| author_facet | Du, Wenkui Yi, Yuchao Zhao, Ziyi |
| contents | In this paper, we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in $\mathbb{R}^{n+m}$, where we associate a nonnegative anisotropic weight $Φ: S^{n+m-1}\to \mathbb{R}^{+}$ to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m=1, 2$ and $Φ$ is the support function of ellipsoids or certain type of centrally symmetric long convex bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wulff inequality for minimal submanifolds in Euclidean space Du, Wenkui Yi, Yuchao Zhao, Ziyi Differential Geometry In this paper, we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in $\mathbb{R}^{n+m}$, where we associate a nonnegative anisotropic weight $Φ: S^{n+m-1}\to \mathbb{R}^{+}$ to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m=1, 2$ and $Φ$ is the support function of ellipsoids or certain type of centrally symmetric long convex bodies. |
| title | Wulff inequality for minimal submanifolds in Euclidean space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2412.19063 |