2n 球中嵌入常均匀性高维环面

Brendle 证明了关于在圆三维球中嵌入的最小环面的 Lawson 猜想。Carlotto 和 Schulz 在圆四维球中构造了一个最小嵌入的三维环面，并 conjectured 该环面是圆四维球中唯一的最小嵌入的三维环面。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 $\mathbb{S}^{2n}(1)$.