Some rigidity results for static three-manifolds with boundary and positive scalar curvature
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918156726960128 |
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| author | Medvedev, Vladimir |
| author_facet | Medvedev, Vladimir |
| contents | This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary $Nar_{-1,1}(\mathbb S^2)$ is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect the boundary. We also establish a rigidity theorem for the upper hemisphere with the standard static potential, in the spirit of Cruz and Nunes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some rigidity results for static three-manifolds with boundary and positive scalar curvature Medvedev, Vladimir Differential Geometry This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary $Nar_{-1,1}(\mathbb S^2)$ is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect the boundary. We also establish a rigidity theorem for the upper hemisphere with the standard static potential, in the spirit of Cruz and Nunes. |
| title | Some rigidity results for static three-manifolds with boundary and positive scalar curvature |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.07296 |