An Affine-Invariant Metric on the Class of Convex Planar Compacta

Abstract

It is proved that for any two convex compacta $K,K' \subset \mathbb{R}^2$, there exist affine transformations T₁ and T₂ such that T₁(K)⊂K′⊂T₂(K) and $S(T_1(K))> \tfrac{16}{111}S((T_2(K))$, where $S(\cdot)$ is the area. Bibliography: 1 title.