L. Alías

A short proof of Bernstein's theorem via the Omori--Yau maximum principle

We give a short, self-contained proof of Bernstein's theorem: every entire minimal graph in $R^3$ is a plane. The only global tool is the Omori-Yau maximum principle, which holds on entire minimal graphs with their induced metric. We apply it exactly once to a single explicit function $F$ built from the surface's angle...