Recent progress in isoparametric functions and isoparametric hypersurfaces

摘要

This paper gives a survey of recent progress in isoparametric functions andisoparametric hypersurfaces, mainly in two directions. (1) Isoparametricfunctions on Riemannian manifolds, including exotic spheres. The existences andnon-existences will be considered. (2) The Yau conjecture on the firsteigenvalues of the embedded minimal hypersurfaces in the unit spheres. Thehistory and progress of the Yau conjecture on minimal isoparametrichypersurfaces will be stated.