一般凸体与单形间Banach-Mazur距离估计的一种简单方法(英文)

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 sup_(C∈K^n) d_(BM)(C,△)≤n + 2,where d_(BM)(.,.) denotes the Banach-Mazur distance,A denotes an n-dimensional simplex and K^n denotes the class of n-dimensional convex sets in R^n.