New examples of constant mean curvature hypersurfaces in the sphere

2022/09/27 by Chuqi Huang, Huang, Chuqi, Guoxin Wei +1 · 2 citations
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2209.13236

Abstract

In this paper, firstly, we show the existence of a compact embedded constant mean curvature (CMC) hypersurface Σ₁ in \mathbbS²ⁿ of the type S^n-1 × S^n-1 × S¹. Moreover, the hypersurface Σ₁ exhibits O(n)× O(n) symmetry. Secondly, we show that there exists a compact embedded CMC-hypersurface Σ₂ ⊂ \mathbbS^3n-1 of the type S^n-1 × S^n-1 × S^n-1 × S¹. These results generalize the results of Carlotto and Schulz.

Cited by

• Existence of a constant-mean-curvature hypertorus in \(S⁴\) via computer assistance
• Navigating the Space of Compact CMC Hypersurfaces in Spheres, Part II

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