Verstraelen's isoparametricity conjecture for minimal hypersurfaces

From papers

Let MnM^{n} be a closed immersed minimal hypersurface of the unit sphere Sn+1\mathbb{S}^{n+1} with constant scalar curvature. A hypersurface is isoparametric if it has constant principal curvatures. Verstraelen's conjecture. MnM^{n} is isoparametric. This is presented as a stronger version of Chern's conjecture, and the source states that all currently known closed minimal hypersurfaces in spheres with constant scalar curvature are isoparametric. The conjecture itself remains open in general.

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Primary source

Chengchao He, Hongwei Xu and Entao Zhao, “Classification of closed minimal hypersurfaces with constant scalar curvature in S^5”, arXiv:2603.01181 (2026).

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