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Recent Progress in Isoparametric Functions and Isoparametric Hypersurfaces

  • Chao Qian
  • Zizhou Tang
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 106)

Abstract

This paper gives a survey of recent progress in isoparametric functions and isoparametric hypersurfaces, mainly in two directions.
  1. (1)

    Isoparametric functions on Riemannian manifolds, including exotic spheres. The existences and non-existences will be considered.

     
  2. (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.

     

Keywords

Riemannian Manifold Unit Sphere Complete Riemannian Manifold Positive Scalar Curvature Isoparametric Hypersurface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical Sciences, Laboratory of Mathematics and Complex SystemsBeijing Normal UniversityBeijingChina

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