Let n≥2 and let Φ:Rn→[0,∞) be a positively
1-homogeneous and convex function. Given two convex bodies A⊂B in
Rn, the monotonicity of anisotropic Φ-perimeters holds, i.e.
PΦ(A)≤PΦ(B). In this note, we prove a quantitative lower bound on
the difference of the Φ-perimeters of A and B in terms of their
Hausdorff distance.Comment: 8 page