A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912374787670016 |
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| author | Chai, Xiaoxiang Chen, Yimin |
| author_facet | Chai, Xiaoxiang Chen, Yimin |
| contents | We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from a star-shaped initial hypersurface. We prove the long-time existence of the flow and its uniform convergence to a $θ$-totally umbilical cap. Additionally, we establish that a $θ$-totally umbilical cap is an energy minimizer for a given enclosed volume. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06934 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane Chai, Xiaoxiang Chen, Yimin Differential Geometry Primary: 53E10, Secondary: 35K93 We prove a new Minkowski type formula for capillary hypersurfaces supported on totally geodesic hyperplanes in hyperbolic space. It leads to a volume-preserving flow starting from a star-shaped initial hypersurface. We prove the long-time existence of the flow and its uniform convergence to a $θ$-totally umbilical cap. Additionally, we establish that a $θ$-totally umbilical cap is an energy minimizer for a given enclosed volume. |
| title | A Constrained Mean Curvature Flow On Capillary Hypersurface Supported On Totally Geodesic Plane |
| topic | Differential Geometry Primary: 53E10, Secondary: 35K93 |
| url | https://arxiv.org/abs/2405.06934 |