New area-minimizing Lawson-Osserman cones

It has been 40 years since Lawson and Osserman introduced the three minimal cones associated with Dirichlet problems in their 1977 Acta paper [13]. The first cone was shown area-minimizing by Harvey and Lawson in the celebrated paper [10]. 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 [26] is area-minimizing.