Isoparametric foliation and Yau conjecture on the first eigenvalue

Details Isoparametric foliation and Yau conjecture on the first eigenvalue Isoparametric foliation and Yau conjecture on the first eigenvalue

2012-01-03

arxiv.org/abs/1201.0666v2

Mathematics

Differential Geometry

Scientific paper

A well known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface $M^n$ in the unit sphere $S^{n+1}(1)$ is just its dimension $n$. The present paper shows that Yau conjecture is true for minimal isoparametric hypersurfaces. Moreover, the more fascinating result of this paper is that the first eigenvalues of the focal submanifolds are equal to their dimensions in the non-stable range.

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