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Isoparametric hypersurfaces with four principal curvatures, IV

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arxiv 1605.00976 v2 pith:6SH7ZAMI submitted 2016-05-03 math.DG

Quo-Shin Chi This is my paper · ORCID
classification math.DG
keywords isoparametricconstructedcurvaturesfourhypersurfacesprincipalcartanclassification
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abstract

We prove that an isoparametric hypersurface with four principal curvatures and multiplicity pair $(7,8)$ is either the one constructed by Ozeki and Takeuchi, or one of the two constructed by Ferus, Karcher, and M\"{u}nzner. This completes the classification of isoparametric hypersurfaces in spheres that \'{E}. Cartan initiated in the late 1930s.

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  1. Supercritical elliptic problems on the round sphere and nodal solutions to the Yamabe problem in projective spaces

    math.AP 2019-08 conditional novelty 6.0 of 10

    For isoparametric functions on spheres, the authors construct infinite nodal solutions to semilinear Yamabe-type equations for subcritical, critical, and supercritical exponents, with blow-up on focal submanifolds.

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