Calculus of Variations and Geometric Measure Theory

G. Saracco - G. Stefani

On the monotonicity of weighted perimeters of convex bodies

created by saracco on 13 Jun 2023
modified on 08 Apr 2024


Published Paper

Inserted: 13 jun 2023
Last Updated: 8 apr 2024

Journal: Math. Nachr.
Volume: 297
Number: 4
Pages: 1444--1450
Year: 2024
Doi: 10.1002/mana.202300280

ArXiv: 2306.07770 PDF


We prove that, among weighted isotropic perimeters, only constant multiples of the Euclidean perimeter satisfy the monotonicity property on nested convex bodies. Although the analogous result fails for general weighted anisotropic perimeters, a similar characterization holds for radially-weighted anisotropic densities.

Keywords: weighted perimeter, convex body, monotonicity property