On electrostatic manifolds with boundary
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913827976642560 |
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| author | Demurov, Stanislav Medvedev, Vladimir |
| author_facet | Demurov, Stanislav Medvedev, Vladimir |
| contents | Static manifolds with boundary were recently introduced by Cruz and Vitório in the context of the prescribed scalar curvature problem in a manifold with boundary with prescribed mean curvature. This kind of manifold is also interesting from the point of view of the general theory of relativity. In this article, we introduce electrostatic manifolds with boundary as a natural generalization of static manifolds with boundary in the presence of a non-zero electric field. We study the geometry of the zero-level set of the potential and its connection to the global properties of electrostatic manifolds with boundary. In particular, we establish some rigidity theorems for the 3-dimensional Euclidean ball and for the Reissner-Nordström manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05581 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On electrostatic manifolds with boundary Demurov, Stanislav Medvedev, Vladimir Differential Geometry Mathematical Physics Static manifolds with boundary were recently introduced by Cruz and Vitório in the context of the prescribed scalar curvature problem in a manifold with boundary with prescribed mean curvature. This kind of manifold is also interesting from the point of view of the general theory of relativity. In this article, we introduce electrostatic manifolds with boundary as a natural generalization of static manifolds with boundary in the presence of a non-zero electric field. We study the geometry of the zero-level set of the potential and its connection to the global properties of electrostatic manifolds with boundary. In particular, we establish some rigidity theorems for the 3-dimensional Euclidean ball and for the Reissner-Nordström manifold. |
| title | On electrostatic manifolds with boundary |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2505.05581 |