A Heintze-Karcher type inequality in hyperbolic space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915536074440704 |
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| author | Hu, Yingxiang Wei, Yong Zhou, Tailong |
| author_facet | Hu, Yingxiang Wei, Yong Zhou, Tailong |
| contents | In this paper, we prove a new Heintze-Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov type theorem for closed embedded hypersurfaces with constant shifted $k$th mean curvature in hyperbolic space. Furthermore, a uniqueness result for $h$-convex hypersurfaces satisfying certain curvature equations is obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_14591 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Heintze-Karcher type inequality in hyperbolic space Hu, Yingxiang Wei, Yong Zhou, Tailong Differential Geometry In this paper, we prove a new Heintze-Karcher type inequality for shifted mean convex hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov type theorem for closed embedded hypersurfaces with constant shifted $k$th mean curvature in hyperbolic space. Furthermore, a uniqueness result for $h$-convex hypersurfaces satisfying certain curvature equations is obtained. |
| title | A Heintze-Karcher type inequality in hyperbolic space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2306.14591 |