An inequality for the volume of inscribed ellipsoids

Abstract

Let K be a convex body in Rn, and let x* ∈ int K be the center of the ellipsoid of the maximal volume inscribed in the body. An arbitrary hyperplane through x* cuts K into two convex bodies K+ and K-. We show that w(K±)/w(K)≤0.844..., where w(·) is the volume of the inscribed ellipsoid. © 1990 Springer-Verlag New York Inc.