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.
On the monotonicity of weighted perimeters of convex bodies / Saracco, G.; Stefani, G.. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - ELETTRONICO. - 297:(2024), pp. 1444-1450. [10.1002/mana.202300280]
On the monotonicity of weighted perimeters of convex bodies
Saracco, G.
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2024
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.File in questo prodotto:
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