Serrin-type problem in divergence form on Riemannian manifolds
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912499054411776 |
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| author | Batista, Márcio Santos, Márcio da Silva, Antônio Sindeaux, Joyce |
| author_facet | Batista, Márcio Santos, Márcio da Silva, Antônio Sindeaux, Joyce |
| contents | In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17838 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Serrin-type problem in divergence form on Riemannian manifolds Batista, Márcio Santos, Márcio da Silva, Antônio Sindeaux, Joyce Differential Geometry In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting. |
| title | Serrin-type problem in divergence form on Riemannian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2507.17838 |