Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910917137006592 |
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| author | Chen, Jingche Hong, Han Li, Haizhong |
| author_facet | Chen, Jingche Hong, Han Li, Haizhong |
| contents | In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in $\mathbb{R}^6$ with finite index must be minimal. This provides a positive answer to do Carmo's question in dimension $6$. The proof strategy is also applicable to $\mathbb{R}^4$ and $\mathbb{R}^5$, thereby providing alternative proofs for those previously resolved cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08107 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$ Chen, Jingche Hong, Han Li, Haizhong Differential Geometry 53A10, 53C42 In this paper, we prove that complete noncompact constant mean curvature hypersurfaces in $\mathbb{R}^6$ with finite index must be minimal. This provides a positive answer to do Carmo's question in dimension $6$. The proof strategy is also applicable to $\mathbb{R}^4$ and $\mathbb{R}^5$, thereby providing alternative proofs for those previously resolved cases. |
| title | Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$ |
| topic | Differential Geometry 53A10, 53C42 |
| url | https://arxiv.org/abs/2503.08107 |