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
Abstract:
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
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