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Characterization Of Simplices Via The Bezout Inequality For Mixed Volumes, Christos Saroglou, Ivan Soprunov, Arten Zvavitch
Characterization Of Simplices Via The Bezout Inequality For Mixed Volumes, Christos Saroglou, Ivan Soprunov, Arten Zvavitch
Mathematics and Statistics Faculty Publications
We consider the following Bezout inequality for mixed volumes: V (K1, . . . ,Kr, Δ[n − r])Vn(Δ)r−1 ≤ r i=1 V (Ki, Δ[n − 1]) for 2 ≤ r ≤ n. It was shown previously that the inequality is true for any -dimensional simplex and any convex bodies in . It was conjectured that simplices are the only convex bodies for which the inequality holds for arbitrary bodies in . In this paper we prove that this is indeed the case if we assume that is a convex polytope. Thus the Bezout inequality characterizes simplices in the class of …