New area-minimizing Lawson-Osserman cones

TL;DR

This paper proves that all Lawson-Osserman cones of type (n, p, 2), previously constructed, are area-minimizing, extending the known minimality results for these classical cones over the past four decades.

Contribution

It establishes the area-minimizing property for the remaining Lawson-Osserman cones of type (n, p, 2), completing the classification of their minimality.

Findings

All Lawson-Osserman cones of type (n, p, 2) are area-minimizing.

Confirms the minimality of previously unproven cones.

Extends classical results on minimal cones from 1977 to new cases.

Abstract

It has been 40 years since Lawson and Osserman introduced the three minimal cones associated with Dirichlet problems in their 1977 Acta paper [LO77]. The first cone was shown area-minimizing by Harvey and Lawson in the celebrated paper [HL82]. In this paper, we confirm that the other two are also area-minimizing. In fact, we show that every Lawson-Osserman cone of type (n, p, 2) constructed in [XYZ] is area-minimizing.