Recent Progress in Isoparametric Functions and Isoparametric Hypersurfaces

Chao Qian,Zizhou Tang

doi:10.1007/978-4-431-55215-4_6

Recent Progress in Isoparametric Functions and Isoparametric Hypersurfaces

Chao Qian, Zizhou Tang

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https://doi.org/10.1007/978-4-431-55215-4_6

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Publication Date: Jan 1, 2014

Citations: 34

Affiliation: University of Chinese Academy of Sciences, Beijing Normal University

#Isoparametric Functions #Yau Conjecture + Show 6 more

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Abstract

This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions. (1) Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and non-existences will be considered. (2) The Yau conjecture on the first eigenvalues of the embedded minimal hypersurfaces in the unit spheres. The history and progress of the Yau conjecture on minimal isoparametric hypersurfaces will be stated.

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