Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4
Differential Geometry
2025-01-07 v2
Abstract
In this paper we study the geometry of complete constant mean curvature (CMC) hypersurfaces immersed in an (n + 1)-dimensional Riemannian manifold N (n = 2, 3 and 4) with sectional curvatures uniformly bounded from below. We generalise radius estimates given by Rosenberg [32] (n = 2) and by Elbert, Nelli and Rosenberg [13] and Cheng [2] (n = 3, 4) to nearly stable CMC hypersurfaces immersed in N. We also prove that certain CMC hypersurfaces effectively embedded in N must be proper.
Cite
@article{arxiv.2411.02151,
title = {Radius estimates for nearly stable H-hypersurfaces of dimension 2, 3, and 4},
author = {Giuseppe Tinaglia and Alex Zhou},
journal= {arXiv preprint arXiv:2411.02151},
year = {2025}
}
Comments
17 pages. Citation added. Accepted for publication in the Journal of Topology and Analysis