A C2-Perturbative Bernstein Theorem for Anisotropic Entire Minimal Graphs
Lu Chen, Jiali Lan
Abstract
We prove a Bernstein theorem for Φ-anisotropic minimal hypersurfaces in dimensions 1≤ n≤ 7 that the only entire smooth solutions u of Φ-anisotropic minimal hypersurfaces equation are affine functions provided the anisotropic area functional integrand Φ is sufficiently C2--close to the Euclidean area integrand. This settles the C2 entire--graph version of anisotropic Bernstein problem posed by Mooney and Yang MooneyYang2024, and the proof uses a compactness--rigidity argument combined with Figalli's regularity theorem established in Figalli2017.
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