Stable anisotropic minimal hypersurfaces in ${\mathbb{R}}^5$ and ${\mathbb{R}}^6$

In this paper, we prove that a complete, two-sided, stable anisotropic minimal immersed hypersurface in ${\mathbb{R}}^5$ or ${\mathbb{R}}^6$ is flat, provided the anisotropic area functional is $C^4$-close to the area functional.