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Isoparametric foliation and Yau conjecture on the first eigenvalue, II

This is a continuation of [23], which investigated the first eigenvalues of minimal isoparametric hypersurfaces with g=4 distinct principal curvatures and focal submanifolds in unit spheres. For the focal submanifolds with g=6, the present paper obtains estimates on all the eigenvalues, among others...

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Bibliographic Details
Published in:Journal of functional analysis 2014-05, Vol.266 (10), p.6174-6199
Main Authors: Tang, Zizhou, Xie, Yuquan, Yan, Wenjiao
Format: Article
Language:English
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Summary:This is a continuation of [23], which investigated the first eigenvalues of minimal isoparametric hypersurfaces with g=4 distinct principal curvatures and focal submanifolds in unit spheres. For the focal submanifolds with g=6, the present paper obtains estimates on all the eigenvalues, among others, giving an affirmative answer in one case to the problem posed in [23], which may be regarded as a generalization of Yau's conjecture. In two of the four unsettled cases in [23] for focal submanifolds M1 of OT-FKM-type, we prove the first eigenvalues to be their respective dimensions.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2014.02.024