, Volume 39, Issue 2, pp 213-222

Restricted chord projection and affine inequalities

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Abstract

It is proved that if ∏*K is the polar projection body of a convex body K in R n , then the volumes of K and ∏*K satisfy the inequality $$V(K)^{n - 1} V(\Pi *K) \geqslant \frac{{(2n)!}}{{n^n \left( {n!} \right)^2 }},$$ with equality if and only if K is a simplex. A new zonoid, called the mean zonoid, is defined and some inequalities which characterize the simplices are also proved.