On FKM isoparametric hypersurfaces in \mathbbSⁿ × \mathbbSⁿ and new area-minimizing cones

2025/10/16 by Cui, Hongbin
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.14650

Abstract

Via a new isoparametric foliation in \mathbbSⁿ(1) × \mathbbSⁿ(1), we find many new area-minimizing cones by applying Lawlor's curvature criterion, especially codimension-two area-minimizing cones in ℝ²ⁿ⁺² for n≥ 63. This new isoparametric foliation is a further restriction of the Ferus-Karcher-Münzner isoparametric foliation to \mathbbSⁿ(1) × \mathbbSⁿ(1) ⊂ \mathbbS²ⁿ⁺¹(√(2)), which can also be defined on general \mathbbSⁿ(a) × \mathbbSⁿ(b)(a>0,b>0), and it extends the recent classification results of F. Urbano for n=2.

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Related

• Minimizing cones associated with isoparametric foliations
• Clifford algebra, isoparametric foliation and related geometric constructions
• Regularity of minimal surfaces near quadratic cones
• Isoparametric foliations of Sⁿ× Sⁿ of codimension 1
• On the Work of Cartan and Münzner on Isoparametric Hypersurfaces