Isoparametric foliation and Yauconjecture on the first eigenvalue

A well-known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface Mⁿ in the unit sphere Sⁿ⁺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.