Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914006461054976 |
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| author | Cheng, Qing-Ming Peng, Yejuan |
| author_facet | Cheng, Qing-Ming Peng, Yejuan |
| contents | In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in $H^{4}(-1)$ satisfies $S\leq \frac{21}{29}$ by making use of the Generalized Maximum Principle, where $S$ denotes the squared norm of the second fundamental form of the hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$ Cheng, Qing-Ming Peng, Yejuan Differential Geometry In this paper, we study $n$-dimensional complete minimal hypersurfaces in a hyperbolic space $H^{n+1}(-1)$ of constant curvature $-1$. We prove that a $3$-dimensional complete minimal hypersurface with constant scalar curvature in $H^{4}(-1)$ satisfies $S\leq \frac{21}{29}$ by making use of the Generalized Maximum Principle, where $S$ denotes the squared norm of the second fundamental form of the hypersurface. |
| title | Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2407.05406 |