On p-Brunn-Minkowski inequalities for intrinsic volumes with 0≤ p<1

2021/07/02 by Chiara Bianchini, Andrea Colesanti, Bianchini, C. +5
Mathematics · #Analytic and geometric function theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2107.01287

openalex publication_date 2021/07/02 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We prove the validity of the p-Brunn-Minkowski inequality for the intrinsic volume V_k, k=2,…, n-1, of convex bodies in ℝⁿ, in a neighborhood of the unit ball, for 0≤ p&lt;1. We also prove that this inequality does not hold true on the entire class of convex bodies of ℝⁿ, when p is sufficiently close to 0.

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