On the monotonicity of weighted perimeters of convex bodies

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 an...

Full description

Saved in:
Bibliographic Details
Published in:Mathematische Nachrichten 2024-04, Vol.297 (4), p.1444-1450
Main Authors: Saracco, Giorgio, Stefani, Giorgio
Format: Article
Language:English
Subjects:
convex body
monotonicity property
weighted perimeter
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202300280