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 $\mathbb{R}^{n},\, n \geq 8$.