Minimizing cones associated with isoparametric foliations

TL;DR

This paper introduces new classes of minimal cones derived from isoparametric foliations on spheres, demonstrating their minimizing properties in most dimensions, thus expanding understanding of minimal surface structures.

Contribution

The paper constructs new minimal cones over focal submanifolds and their products, proving their minimizing nature in higher dimensions, which was previously unknown.

Findings

New series of minimizing cones over focal submanifolds

Minimizing cones over certain product manifolds

Most of these cones are proven minimizing except in low dimensions

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.