A Frankel type theorem in Euclidean and hyperbolic spaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866916055149969408 |
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| author | Xue, Haotian |
| author_facet | Xue, Haotian |
| contents | We prove that a connected mean convex region in $\mathbb{R}^{n+1}$ with at least two components cannot have strictly positive mean curvature. This answers a question of Gromov. We also obtain estimates for how quickly the mean curvature must decay at infinity, and generalize this result to hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19679 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Frankel type theorem in Euclidean and hyperbolic spaces Xue, Haotian Differential Geometry We prove that a connected mean convex region in $\mathbb{R}^{n+1}$ with at least two components cannot have strictly positive mean curvature. This answers a question of Gromov. We also obtain estimates for how quickly the mean curvature must decay at infinity, and generalize this result to hyperbolic space. |
| title | A Frankel type theorem in Euclidean and hyperbolic spaces |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.19679 |