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; Pagnini, D; Roncoroni, A. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - ELETTRONICO. - (2022), pp. 0-0. [10.1007/s00208-022-02454-0]
On p-Brunn-Minkowski inequalities for intrinsic volumes, with 0 <= p < 1
Bianchini, C
;Colesanti, A;Pagnini, D;Roncoroni, A
2022
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.
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