A note on the anisotropic Bernstein problem in ℝ³

Rosales, César

doi:10.1090/bproc/214

A note on the anisotropic Bernstein problem in ${\mathbb {R}}^3$
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by César Rosales;

Proc. Amer. Math. Soc. Ser. B 11 (2024), 105-114

DOI: https://doi.org/10.1090/bproc/214

Published electronically: May 15, 2024

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Abstract:

It was proved by Jenkins [Arch. Rational Mech. Anal. 8 (1961), 181–206] that a smooth entire graph in ${\mathbb {R}}^3$ 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.

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Proceedings of the American Mathematical Society Series B

A note on the anisotropic Bernstein problem in ${\mathbb {R}}^3$
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Abstract: