Rigidity and compactness with constant mean curvature in warped product manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916896401522688 |
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| author | Maggi, Francesco Santilli, Mario |
| author_facet | Maggi, Francesco Santilli, Mario |
| contents | We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and Reissner--Nordstrom manifolds). As a corollary we characterize limits of rectifiable boundaries whose mean curvatures converge, as distributions, to a constant. The latter result is new, and requires the full strength of distributional CMC-rigidity, even when one considers smooth boundaries whose mean curvature oscillations vanish in arbitrarily strong $C^k$-norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03499 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Rigidity and compactness with constant mean curvature in warped product manifolds Maggi, Francesco Santilli, Mario Differential Geometry Analysis of PDEs We prove the rigidity of rectifiable boundaries with constant distributional mean curvature in the Brendle class of warped product manifolds (which includes important models in General Relativity, like the deSitter--Schwarzschild and Reissner--Nordstrom manifolds). As a corollary we characterize limits of rectifiable boundaries whose mean curvatures converge, as distributions, to a constant. The latter result is new, and requires the full strength of distributional CMC-rigidity, even when one considers smooth boundaries whose mean curvature oscillations vanish in arbitrarily strong $C^k$-norms. |
| title | Rigidity and compactness with constant mean curvature in warped product manifolds |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2303.03499 |