English

Recent progress in isoparametric functions and isoparametric hypersurfaces

Differential Geometry 2014-06-13 v3

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.

Keywords

Cite

@article{arxiv.1403.6980,
  title  = {Recent progress in isoparametric functions and isoparametric hypersurfaces},
  author = {Chao Qian and Zizhou Tang},
  journal= {arXiv preprint arXiv:1403.6980},
  year   = {2014}
}

Comments

12 pages, to appear in the ICM 2014 Satellite Conference on Real & Complex Submanifolds Springer Proceedings in Mathematics. References are updated

R2 v1 2026-06-22T03:35:51.740Z