On Lawson's area-minimizing hypercones

TL;DR

This paper proves that all homogeneous area-minimizing hypercones in Euclidean spaces are indeed area-minimizing and possess calibrations singular only at the origin, extending Lawson's classification and ideas.

Contribution

It establishes the area-minimality of all Lawlor-classified hypercones and demonstrates their calibrations are singular only at the origin, building on Lawson's original approach.

Findings

All homogeneous area-minimizing hypercones are area-minimal.

Each hypercone admits a (coflat) calibration singular only at the origin.

The results extend Lawson's classification and original ideas.

Abstract

We show the area-minimality property of all homogeneous area-minimizing hypercones in Euclidean spaces (classified by Lawlor) following Lawson's original idea in his 72' Trans. A.M.S. paper "The equivariant Plateau problem and interior regularity". Moreover, each of them enjoys (coflat) calibrations singular only at the origin.