Small spheres with prescribed nonconstant mean curvature in Riemannian 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_ | 1866916120171118592 |
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| author | Enciso, Alberto Fernández, Antonio J. Peralta-Salas, Daniel |
| author_facet | Enciso, Alberto Fernández, Antonio J. Peralta-Salas, Daniel |
| contents | Given a function $f$ on a smooth Riemannian manifold without boundary, we prove that if $p \in M$ is a non-degenerate critical point of $f$, then a neighborhood of $p$ contains a foliation by spheres with mean curvature proportional to $f$. This foliation is essentially unique. The nondegeneracy assumption can be substantially relaxed, at the expense of losing the property that the family of spheres with prescribed mean curvature defines a foliation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09809 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds Enciso, Alberto Fernández, Antonio J. Peralta-Salas, Daniel Differential Geometry Analysis of PDEs 53A10, 53C42, 58J05, 58J55 Given a function $f$ on a smooth Riemannian manifold without boundary, we prove that if $p \in M$ is a non-degenerate critical point of $f$, then a neighborhood of $p$ contains a foliation by spheres with mean curvature proportional to $f$. This foliation is essentially unique. The nondegeneracy assumption can be substantially relaxed, at the expense of losing the property that the family of spheres with prescribed mean curvature defines a foliation. |
| title | Small spheres with prescribed nonconstant mean curvature in Riemannian manifolds |
| topic | Differential Geometry Analysis of PDEs 53A10, 53C42, 58J05, 58J55 |
| url | https://arxiv.org/abs/2302.09809 |