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.