Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I

Fuente: arXiv
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Main Author: Perdomo, Oscar
Format: Preprint
Published: 2025
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author Perdomo, Oscar
author_facet Perdomo, Oscar
contents In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples with $H=0$, we verify Yau's conjecture stating that among the embedded, non-totally umbilical minimal hypersurfaces in spheres, the Clifford hypersurfaces have the least area.
format Preprint
id arxiv_https___arxiv_org_abs_2503_13823
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I
Perdomo, Oscar
Differential Geometry
53C42
In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples with $H=0$, we verify Yau's conjecture stating that among the embedded, non-totally umbilical minimal hypersurfaces in spheres, the Clifford hypersurfaces have the least area.
title Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I
topic Differential Geometry
53C42
url https://arxiv.org/abs/2503.13823