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,△)≤...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.展开更多
文摘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.
基金Supported by the National Natural Science Foundation of China (11001134 , 11126250)the Fundamental Research Funds for the Central Universitiesthe Tianjin Science & Technology Fund (20100820)
基金Supported by the National Natural Science Foundation of China(11671122)Key Scientific and Technological Project of Henan Province(162102210069)Key Scientific Research Project for Colleges and Universities in Henan Province(15A110031)
