  We show that a complete, two-sided, stable immersed anisotropic minimal
hypersurface in $\mathbf{R}^4$ has intrinsic cubic volume growth, provided the
parametric elliptic integral is $C^2$-close to the area functional. We also
obtain an interior volume upper bound for stable anisotropic minimal
hypersurfaces in the unit ball. We can estimate the constants explicitly in all
of our results.
  In particular, this paper gives an alternative proof of our recent stable
Bernstein theorem for minimal hypersurfaces in $\mathbf{R}^4$. The new proof is
more closely related to techniques from the study of strictly positive scalar
curvature.
