Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I
Differential Geometry
2025-03-19 v1
Abstract
In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the -dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples with , we verify Yau's conjecture stating that among the embedded, non-totally umbilical minimal hypersurfaces in spheres, the Clifford hypersurfaces have the least area.
Keywords
Cite
@article{arxiv.2503.13823,
title = {Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I},
author = {Oscar Perdomo},
journal= {arXiv preprint arXiv:2503.13823},
year = {2025}
}
Comments
21 pages, 7 figures and one table