Uniqueness of Hypersurfaces of Constant Higher Order Mean Curvature in Hyperbolic Space
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866929642774986752 |
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| author | Nelli, Barbara Zhu, Jingyong |
| author_facet | Nelli, Barbara Zhu, Jingyong |
| contents | We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean curvature. Then we prove two Bernstein type results for immersed hypersurfaces under different assumptions. Last, we show the rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_11018 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Uniqueness of Hypersurfaces of Constant Higher Order Mean Curvature in Hyperbolic Space Nelli, Barbara Zhu, Jingyong Differential Geometry We study the uniqueness of horospheres and equidistant spheres in hyperbolic space under different conditions. First we generalize the Bernstein theorem by Do Carmo and Lawson to the embedded hypersurfaces with constant higher order mean curvature. Then we prove two Bernstein type results for immersed hypersurfaces under different assumptions. Last, we show the rigidity of horospheres and equidistant spheres in terms of their higher order mean curvatures. |
| title | Uniqueness of Hypersurfaces of Constant Higher Order Mean Curvature in Hyperbolic Space |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2008.11018 |