An Alternative for Constant Mean Curvature Hypersurfaces
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912002094399488 |
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| author | Mazurowski, Liam Zhou, Xin |
| author_facet | Mazurowski, Liam Zhou, Xin |
| contents | Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean curvature equal to $c$, or there exist infinitely many distinct closed hypersurfaces with constant mean curvature less than $c$ but enclosing half the volume of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13864 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Alternative for Constant Mean Curvature Hypersurfaces Mazurowski, Liam Zhou, Xin Differential Geometry 53A10 Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean curvature equal to $c$, or there exist infinitely many distinct closed hypersurfaces with constant mean curvature less than $c$ but enclosing half the volume of $M$. |
| title | An Alternative for Constant Mean Curvature Hypersurfaces |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/2408.13864 |