If a convex body K in \({\mathbb R}^n\) is contained in a convex body L of elliptic type (a curvature image), then it is known that the affine surface area of K is not larger than the affine surface area of L. We prove that the affine surface areas of K and L can only be equal if K = L.
['Rolf Schneider']
Affine surface area and convex bodies of elliptic type