On a question of S. S. Chern concerning minimal hypersurfaces of spheres (Q2735662)
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scientific article; zbMATH DE number 1641137
| Language | Label | Description | Also known as |
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| English | On a question of S. S. Chern concerning minimal hypersurfaces of spheres |
scientific article; zbMATH DE number 1641137 |
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4 September 2001
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minimal hypersurfaces
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constant scalar curvature
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isoparametric hypersurface
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On a question of S. S. Chern concerning minimal hypersurfaces of spheres (English)
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A famous conjecture by S. S. Chern states that for a compact minimal hypersurface in a unit sphere with constant scalar curvature \(S\), \(S\) belongs to a finite set. A stronger version of this conjecture states that a compact minimal hypersurface with constant scalar curvature \(S\) is isoparametric. In the present paper, the authors sketch a technique which, together with suitable additional assumptions on the numbers and the multiplicities of the principal curvatures, could be used to prove special cases of the previously mentioned conjectures.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00038].
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