Open Access
July 2013 Isoparametric foliation and Yau conjecture on the first eigenvalue
Zizhou Tang, Wenjiao Yan
J. Differential Geom. 94(3): 521-540 (July 2013). DOI: 10.4310/jdg/1370979337


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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Zizhou Tang. Wenjiao Yan. "Isoparametric foliation and Yau conjecture on the first eigenvalue." J. Differential Geom. 94 (3) 521 - 540, July 2013.


Published: July 2013
First available in Project Euclid: 11 June 2013

zbMATH: 1277.53058
MathSciNet: MR3080491
Digital Object Identifier: 10.4310/jdg/1370979337

Rights: Copyright © 2013 Lehigh University

Vol.94 • No. 3 • July 2013
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