Characterizing addition of convex sets by polynomiality of volume and by the homothety operation

DOI10.1142/S0219199714500229zbMath1316.52004MaRDI QIDQ4983012

Liran Rotem, Vitali D. Milman

Publication date: 14 April 2015

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

zbMATH Keywords

volumeconvex setsMinkowski addition

Mathematics Subject Classification ID

Mixed volumes and related topics in convex geometry (52A39) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (4)

Characterizing the Radial Sum for Star Bodies ⋮ Minkowski valuations under volume constraints ⋮ The role of the Rogers-Shephard inequality in the characterization of the difference body ⋮ Minkowski additive operators under volume constraints

Cites Work

• Unnamed Item
• Operations between sets in geometry
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• Mixed integrals and related inequalities
• A characterization of Blaschke addition
• On the distribution function of additive functions
• A New Proof of Erdos's Theorem on Monotone Multiplicative Functions
• Polar Means of Convex Bodies and a Dual to the Brunn-Minkowski Theorem
• $p$-Means of Convex Bodies.

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