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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.14650 |
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| _version_ | 1866917237722447872 |
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| author | Cui, Hongbin |
| author_facet | Cui, Hongbin |
| contents | We present two generalizations for the celebrated works of Ferus-Karcher-Münzner \cite{FKM81} and Wang \cite{W94}. We first show that an isoparametric foliation on $\mathbb{S}^{2n+1}$ constructed by Ferus-Karcher-Münzner naturally yields an isoparametric foliation on its submanifold $\mathbb{S}^n \times \mathbb{S}^n$ with one same focal variety. The second part concerns area-minimizing cones; all known regular area-minimizing hypercones are realized as real algebraic varieties: isoparametric cones (cf. \cite{W94}). As a noteworthy application, we extend area-minimizing isoparametric hypercones in \cite{W94} to codimension-two cases, and obtain infinitely many families (each containing infinitely many members) of area-minimizing subcones of Simons cones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14650 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On FKM isoparametric hypersurfaces in $\mathbb{S}^n \times \mathbb{S}^n$ and new area-minimizing cones Cui, Hongbin Differential Geometry We present two generalizations for the celebrated works of Ferus-Karcher-Münzner \cite{FKM81} and Wang \cite{W94}. We first show that an isoparametric foliation on $\mathbb{S}^{2n+1}$ constructed by Ferus-Karcher-Münzner naturally yields an isoparametric foliation on its submanifold $\mathbb{S}^n \times \mathbb{S}^n$ with one same focal variety. The second part concerns area-minimizing cones; all known regular area-minimizing hypercones are realized as real algebraic varieties: isoparametric cones (cf. \cite{W94}). As a noteworthy application, we extend area-minimizing isoparametric hypercones in \cite{W94} to codimension-two cases, and obtain infinitely many families (each containing infinitely many members) of area-minimizing subcones of Simons cones. |
| title | On FKM isoparametric hypersurfaces in $\mathbb{S}^n \times \mathbb{S}^n$ and new area-minimizing cones |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.14650 |