Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912332093849600 |
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| author | Sun, Chengzhang |
| author_facet | Sun, Chengzhang |
| contents | For a parabolically convex domain $M\subseteq \mathbb{H}^n$, $n\ge 3$, we prove that if $f:(N,\bar g)\to (M,g)$ has nonzero degree, where $N$ is spin with scalar curvature $R_N\ge -n(n-1)$, and if $f|_{\partial N}$ does not increase the distance and the mean curvature, then $N$ is hyperbolic, and $\partial N$ is isometric to $\partial M$. This is a partial generalization of Lott's result \cite{lott2021index} to negative lower bounds of scalar curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09290 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces Sun, Chengzhang Differential Geometry For a parabolically convex domain $M\subseteq \mathbb{H}^n$, $n\ge 3$, we prove that if $f:(N,\bar g)\to (M,g)$ has nonzero degree, where $N$ is spin with scalar curvature $R_N\ge -n(n-1)$, and if $f|_{\partial N}$ does not increase the distance and the mean curvature, then $N$ is hyperbolic, and $\partial N$ is isometric to $\partial M$. This is a partial generalization of Lott's result \cite{lott2021index} to negative lower bounds of scalar curvature. |
| title | Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2411.09290 |