Rigidity of spacelike hypersurface with constant curvature and intersection angle condition
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911516453765120 |
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| author | Gao, Shanze |
| author_facet | Gao, Shanze |
| contents | In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. The proof is based on an auxiliary function and associated integral equality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_17410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rigidity of spacelike hypersurface with constant curvature and intersection angle condition Gao, Shanze Differential Geometry 53C50, 53C42, 35N25 In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane with constant intersection angles, then the hypersurface must be a part of a hyperboloid, unless it is entirely contained in the hyperplane. The proof is based on an auxiliary function and associated integral equality. |
| title | Rigidity of spacelike hypersurface with constant curvature and intersection angle condition |
| topic | Differential Geometry 53C50, 53C42, 35N25 |
| url | https://arxiv.org/abs/2412.17410 |