A note on the anisotropic Bernstein problem in ℝ³

Abstract

It was proved by Jenkins [Arch. Rational Mech. Anal. 8 (1961), 181–206] that a smooth entire graph in R 3 {\mathbb {R}}^3 with vanishing anisotropic mean curvature must be a plane. By using a calibration argument and a stability inequality we show here a different self-contained proof of this result, which is still valid when the anisotropic mean curvature is constant.