Every stationary polyhedral set in \(\mathbb{R}^ n\) is area minimizing under diffeomorphisms (Q1816508)

There are infinitely many minimal cones in \(\mathbb{R}^3\). Of these only three are area minimizing under Lipschitz maps: the plane; the three half planes meeting along their common boundary line at an angle of 120 degrees; the cone over the one-skeleton of the regular tetrahedron. In this paper we prove that every stationary polyhedral set in \(\mathbb{R}^n\) is area minimizing under diffeomorphisms leaving the boundary fixed. This theorem is also extended to the surface energy of crystals and immiscible fluids.