Isoparametric foliation and yau conjecture on the first eigenvalue

Zizhou Tang Beijing Normal University Wenjiao Yan Beijing Normal University

Differential Geometry mathscidoc:1609.10323

Journal of Differential Geometry, 94, (3), 521-540, 2013
A well-known conjecture of Yau states that the first eigenvalue of every closed minimal hypersurface Mn 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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@inproceedings{zizhou2013isoparametric,
  title={ISOPARAMETRIC FOLIATION AND YAU CONJECTURE ON THE FIRST EIGENVALUE},
  author={Zizhou Tang, and Wenjiao Yan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914081157745907985},
  booktitle={Journal of Differential Geometry},
  volume={94},
  number={3},
  pages={521-540},
  year={2013},
}
Zizhou Tang, and Wenjiao Yan. ISOPARAMETRIC FOLIATION AND YAU CONJECTURE ON THE FIRST EIGENVALUE. 2013. Vol. 94. In Journal of Differential Geometry. pp.521-540. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160914081157745907985.
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