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arXiv · 2311.00166

Flatness of anisotropic minimal graphs in $\mathbb{R}^{n+1}$

Wenkui Du·Yang Yang
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Abstract

We prove a Bernstein theorem for $Φ$-anisotropic minimal hypersurfaces in all dimensional Euclidean spaces that the only entire smooth solutions $u: \mathbb{R}^{n}\rightarrow \mathbb{R}$ of $Φ$-anisotropic minimal hypersurfaces equation are linear functions provided the anisotropic area functional integrand $Φ$ is sufficiently $C^{3}$-close to classical area functional integrand and $|\nabla u(x)|=o(|x|^{\varepsilon})$ for $\varepsilon\leq \varepsilon_{0}(n, Φ)$ with the constant $\varepsilon_{0}(n, Φ)>0$.

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Wenkui Du, Yang Yang. 2024-04-04. Flatness of anisotropic minimal graphs in $\mathbb{R}^{n+1}$. https://arxiv.org/abs/2311.00166

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