  The aim of this note is twofold: to give a short proof of the results in [S.
Larson, A bound for the perimeter of inner parallel bodies, J. Funct. Anal. 271
(2016), 610-619] and [G. Domokos and Z. L\'angi, The isoperimetric quotient of
a convex body decreases monotonically under the eikonal abrasion model,
Mathematika 65 (2019), 119-129]; and to generalize them to the anisotropic
case.
