Anisotropic perimeter and isoperimetric quotient of inner parallel bodies

Abstract

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. Lángi, 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.

5 pages