On the Singular Structure of Three-Dimensional, Area-Minimizing Surfaces

A sufficient condition is given for the union of two three-dimensional planes through the origin in ${{\mathbf {R}}^n}$ to be area-minimizing. The condition is in terms of the three angles $0 \leqslant {\gamma _1} \leqslant {\gamma _2} \leqslant {\gamma _3}$ which characterize the geometric relationship between the planes. If ${\gamma _3} \leqslant {\gamma _1} + {\gamma _2}$, the union of the planes is area-minimizing.