Title: An inequality for the volume of inscribed ellipsoids
Abstract: LetK be a convex body inR n, and letx* ∈ intK be the center of the ellipsoid of the maximal volume inscribed in the body. An arbitrary hyperplane throughx* cutsK into two convex bodiesK + andK −. We show thatw(K ±)/w(K)≤0.844..., wherew(·) is the volume of the inscribed ellipsoid.