Minimizing cones associated with isoparametric foliations

Abstract

Associated with isoparametric foliations of unit spheres, there are two classes of minimal surfaces − minimal isoparametric hypersurfaces and focal submanifolds. By virtue of their rich structures, we find new series of minimizing cones. They are cones over focal submanifolds and cones over suitable products among these two classes. Except in low dimensions, all such cones are shown minimizing.