Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part I
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915203012100096 |
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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 |