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Some new Brunn-Minkowski-type inequalities in convex bodies. (English) Zbl 1121.52024

Summary: We establish some analogues of the Brunn-Minkowski inequalities on convex bodies and the Minkowski inequality and their inverse versions. As an application, we generalize and improve some interrelated results.

MSC:

52A40 Inequalities and extremum problems involving convexity in convex geometry
52A39 Mixed volumes and related topics in convex geometry
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