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arXiv · 2503.13823

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

Oscar Perdomo
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Abstract

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.

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Oscar Perdomo. 2025-03-18. Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I. https://arxiv.org/abs/2503.13823

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