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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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Published in: | Journal of functional analysis 2014-05, Vol.266 (10), p.6174-6199 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0022-1236 1096-0783 |
DOI: | 10.1016/j.jfa.2014.02.024 |