We prove the validity of the p-Brunn-Minkowski inequality for the intrinsic volume V-k, k = 2, ... , n - 1, of symmetric convex bodies in R-n, in a neighbourhood of the unit ball when one of the bodies is the unit ball, for 0 <= p < 1. We also prove that this inequality does not hold true on the entire class of convex bodies of R-n, when p is sufficiently close to 0.
On p-Brunn–Minkowski inequalities for intrinsic volumes, with 0 ≤ p< 1
Bianchini C.;Colesanti A.;Roncoroni A.
2023-01-01
Abstract
We prove the validity of the p-Brunn-Minkowski inequality for the intrinsic volume V-k, k = 2, ... , n - 1, of symmetric convex bodies in R-n, in a neighbourhood of the unit ball when one of the bodies is the unit ball, for 0 <= p < 1. We also prove that this inequality does not hold true on the entire class of convex bodies of R-n, when p is sufficiently close to 0.File in questo prodotto:
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