Embedded constant mean curvature hypertori in the $2n$-sphere

Junqi Lai; Guoxin Wei

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arXiv · 2503.19297

Embedded constant mean curvature hypertori in the $2n$-sphere

Junqi Lai·Guoxin Wei

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Abstract

Brendle proved Lawson conjecture about minimal embedded torus in the round three-dimensional sphere. Carlotto and Schulz constructed a minimal embedded three-dimensional hypertorus in the round four-dimensional sphere and conjectured that their hypertorus is a unique minimal embedded three-dimensional hypertorus in the round four-dimensional sphere. In this paper, we construct two different constant mean curvature embedded $(2n-1)$-dimensional hypertori (that is, topological type $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$) which have the same negative mean curvature $H$ in the round $2n$-dimensional sphere $\mathbb{S}^{2n}(1)$ .

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Junqi Lai, Guoxin Wei. 2025-03-25. Embedded constant mean curvature hypertori in the $2n$-sphere. https://arxiv.org/abs/2503.19297

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