A $C^2$-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs

Lu Chen; Jiali Lan

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arXiv · 2608.29117

A $C^2$-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs

Lu Chen·Jiali Lan

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Abstract

We prove a Bernstein theorem for $\Phi$-anisotropic minimal hypersurfaces in dimensions $1\leq n\leq 7$ that the only entire smooth solutions $u$ of $\Phi$-anisotropic minimal hypersurfaces equation are affine functions provided the anisotropic area functional integrand $\Phi$ is sufficiently $C^{2}$--close to the Euclidean area integrand. This settles the $C^2$ entire--graph version of anisotropic Bernstein problem posed by Mooney and Yang \cite{MooneyYang2024}, and the proof uses a compactness--rigidity argument combined with Figalli's regularity theorem established in \cite{Figalli2017}.

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Lu Chen, Jiali Lan. 2026-08-29. A $C^2$-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs. https://arxiv.org/abs/2608.29117

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