Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds
Differential Geometry
2025-09-15 v1
Abstract
On a finite-volume hyperbolic -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.
Keywords
Cite
@article{arxiv.2509.09881,
title = {Area bounds for constant mean curvature surfaces in hyperbolic 3-manifolds},
author = {Ruojing Jiang},
journal= {arXiv preprint arXiv:2509.09881},
year = {2025}
}