Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909783480598528 |
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| author | Jiang, Ruojing |
| author_facet | Jiang, Ruojing |
| contents | On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies compactness for such surfaces. In particular, for Bryant surfaces with constant mean curvature equal to one, the area is bounded proportionally to the genus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_09881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds Jiang, Ruojing Differential Geometry 53A10 On a finite-volume hyperbolic $3$-manifold, we establish an upper bound on the area of closed embedded surfaces with constant mean curvature at least one, depending on the mean curvature and the genus bounds. This area bound implies compactness for such surfaces. In particular, for Bryant surfaces with constant mean curvature equal to one, the area is bounded proportionally to the genus. |
| title | Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds |
| topic | Differential Geometry 53A10 |
| url | https://arxiv.org/abs/2509.09881 |