Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$

Jingche Chen; Han Hong; Haizhong Li

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arXiv · 2503.08107

Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$

Jingche Chen·Han Hong·Haizhong Li

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Abstract

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.

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BibTeX RIS

Jingche Chen, Han Hong, Haizhong Li. 2025-03-11. Do Carmo's problem for CMC hypersurfaces in $\mathbb{R}^6$. https://arxiv.org/abs/2503.08107

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