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On a Brunn-Minkowski theorem for a geometric domain functional considered by Avhadiev. (English) Zbl 1232.26034

Summary: Suppose two bounded subsets of \(\mathbb{R}^n\) are given. Parametrise the Minkowski combination of these sets by \( t\). The Classical Brunn-Minkowski Theorem asserts that the \( 1/n\)-th power of the volume of the convex combination is a concave function of \( t\). A Brunn-Minkowski-style theorem is established for another geometric domain functional.

MSC:

26D15 Inequalities for sums, series and integrals
52A40 Inequalities and extremum problems involving convexity in convex geometry
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