Volume of the Minkowski sums of star-shaped sets

DOI10.1090/bproc/97zbMath1497.52008arXiv1910.06146OpenAlexW2980305167MaRDI QIDQ5866588

Artem Zvavitch, Matthieu Fradelizi, Zsolt Lángi

Publication date: 22 September 2022

Published in: Proceedings of the American Mathematical Society, Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.06146

zbMATH Keywords

convex hullMinkowski sumstar-shaped set

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Variants of convex sets (star-shaped, ((m, n))-convex, etc.) (52A30)

Related Items (2)

Generalization of Klain’s theorem to Minkowski symmetrization of compact sets and related topics ⋮ Volumes of subset Minkowski sums and the Lyusternik region

Cites Work

• On the analogue of the concavity of entropy power in the Brunn-Minkowski theory
• Do Minkowski averages get progressively more convex?
• A superadditivity and submultiplicativity property for cardinalities of sumsets
• Approximation of points of the convex hull of a sum of sets by points of the sum: an elementary approach
• The convexification effect of Minkowski summation
• Fractional generalizations of Young and Brunn-Minkowski inequalities
• Convex Bodies The Brunn-MinkowskiTheory
• Quasi-Equilibria in Markets with Non-Convex Preferences
• Asymptotic Behavior of Products C p = C + ⋯+ C in Locally Compact Abelian Groups

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