Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866914148138352640 |
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| author | Ding, Qi |
| author_facet | Ding, Qi |
| contents | Let $Σ$ be a complete Riemannian manifold of nonnegative Ricci curvature. We prove a Liouville-type theorem: every smooth solution $u$ to minimal hypersurface equation on $Σ$ is a constant provided $u$ has sublinear growth for its negative part. Here, the sublinear growth condition is sharp. Our proof relies on a gradient estimate for minimal graphs over $Σ$ with small linear growth of the negative parts of graphic functions via iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03394 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature Ding, Qi Differential Geometry Analysis of PDEs Let $Σ$ be a complete Riemannian manifold of nonnegative Ricci curvature. We prove a Liouville-type theorem: every smooth solution $u$ to minimal hypersurface equation on $Σ$ is a constant provided $u$ has sublinear growth for its negative part. Here, the sublinear growth condition is sharp. Our proof relies on a gradient estimate for minimal graphs over $Σ$ with small linear growth of the negative parts of graphic functions via iteration. |
| title | Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2401.03394 |