New examples of constant mean curvature hypersurfaces in the sphere

Chuqi Huang; Guoxin Wei

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arXiv · 2209.13236

New examples of constant mean curvature hypersurfaces in the sphere

Chuqi Huang·Guoxin Wei

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Abstract

In this paper, firstly, we show the existence of a compact embedded constant mean curvature (CMC) hypersurface $\Sigma_1$ in $\mathbb{S}^{2n}$ of the type $S^{n-1} \times S^{n-1} \times S^{1}$. Moreover, the hypersurface $\Sigma_1$ exhibits $O(n)\times O(n)$ symmetry. Secondly, we show that there exists a compact embedded CMC-hypersurface $\Sigma_2 \subset \mathbb{S}^{3n-1}$ of the type $S^{n-1} \times S^{n-1} \times S^{n-1} \times S^{1}$. These results generalize the results of Carlotto and Schulz.

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Chuqi Huang, Guoxin Wei. 2022-09-27. New examples of constant mean curvature hypersurfaces in the sphere. https://arxiv.org/abs/2209.13236

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