On the monotonicity of weighted perimeters of convex bodies

Giorgio Saracco and Giorgio Stefani

Mathematische Nachrichten, 2024, vol. 297, issue 4, 1444-1450

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.

Date: 2024
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