Do Minkowski averages get progressively more convex?

DOI10.1016/j.crma.2015.12.005zbMath1372.52006arXiv1512.03718OpenAlexW2282528246MaRDI QIDQ512347

Artem Zvavitch, Mokshay Madiman, Arnaud Marsiglietti, Matthieu Fradelizi

Publication date: 24 February 2017

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.03718

zbMATH Keywords

Hausdorff distanceMinkowski additionconvexifying operationnon-convexity index

Mathematics Subject Classification ID

Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

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Concentration of information content for convex measures, Weighted Brunn-Minkowski theory. I: On weighted surface area measures, Volumes of subset Minkowski sums and the Lyusternik region, On the volume of the Minkowski sum of zonoids, Two Remarks on Generalized Entropy Power Inequalities, Do Minkowski averages get progressively more convex?, The convexification effect of Minkowski summation, Entropy Inequalities for Sums in Prime Cyclic Groups, Volume of the Minkowski sums of star-shaped sets

Cites Work

• Do Minkowski averages get progressively more convex?
• A superadditivity and submultiplicativity property for cardinalities of sumsets
• A measure of convexity for compact sets
• Fractional generalizations of Young and Brunn-Minkowski inequalities
• Information Inequalities for Joint Distributions, With Interpretations and Applications
• Quasi-Equilibria in Markets with Non-Convex Preferences
• Asymptotic Behavior of Products C p = C + ⋯+ C in Locally Compact Abelian Groups