A half-space Bernstein theorem for anisotropic minimal graphs

Wenkui Du; Connor Mooney; Yang Yang; Jingze Zhu

doi:10.4171/jems/1695

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A half-space Bernstein theorem for anisotropic minimal graphs

Wenkui Du
Massachusetts Institute of Technology, Cambridge, USA
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Connor Mooney
University of California, Irvine, USA
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Yang Yang
Johns Hopkins University, Baltimore, USA
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Jingze Zhu
Massachusetts Institute of Technology, Cambridge, USA
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Abstract

We prove that an anisotropic minimal graph over a half-space with flat boundary must itself be flat. This generalizes a result of Edelen–Wang to the anisotropic case. The proof uses only the maximum principle and ideas from fully nonlinear PDE theory in lieu of a monotonicity formula.

Cite this article

Wenkui Du, Connor Mooney, Yang Yang, Jingze Zhu, A half-space Bernstein theorem for anisotropic minimal graphs. J. Eur. Math. Soc. (2025), published online first

DOI 10.4171/JEMS/1695