A Simple Approach to Estimating the Banach-Mazur Distance between Simplex and Convex Bodies

摘要

We use a simple approach to estimating the Banach-Mazur distance between convex bodies and simplex.As an application of this approach,we provide a purely analytic proof for the known result supC∈κn dBM(C,Δ) ≤ n + 2,where dBM(·,·) denotes the Banach-Mazur distance,Δ denotes an n-dimensional simplex and κn denotes the class of n-dimensional convex sets in Rn.