The anisotropic Bernstein problem

Abstract

We construct nonlinear entire anisotropic minimal graphs over ${\mathbb{R}}^4$, completing the solution to the anisotropic Bernstein problem. The examples we construct have a variety of growth rates, and our approach both generalizes to higher dimensions and recovers and elucidates known examples of entire minimal graphs over ${\mathbb{R}}^n,n\ge 8$.

Final version, to appear in Inventiones Mathematicae