Embedded constant mean curvature hypertori in the 2n-sphere

2025/03/25 by Lai, Junqi, Wei, Guoxin · 1 citation
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.19297

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 \(\mathbbS^n-1 × \mathbbS^n-1 × \mathbbS¹\)) which have the same negative mean curvature \(H\) in the round 2n-dimensional sphere \(\mathbbS²ⁿ(1)\) .

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