一般凸体与单形间Banach-Mazur距离估计的一种简单方法

数学季刊 ›› 2012, Vol. 27 ›› Issue (4): 504-508.

一般凸体与单形间Banach-Mazur距离估计的一种简单方法

Department of Mathematics, Suzhou University of Science and Technology

收稿日期:2011-01-26 出版日期:2012-12-30 发布日期:2023-03-15
作者简介:GUO Qi(1957-), male, native of Jimo, Shandong, a professor of Suzhou University of Science and Technology, Ph.D., engages in functional analysis, convex geometry analysis and mathematical morphology.
基金资助:
Supported by the NNSF of China(11271282)

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

Department of Mathematics, Suzhou University of Science and Technology

Received:2011-01-26 Online:2012-12-30 Published:2023-03-15
About author:GUO Qi(1957-), male, native of Jimo, Shandong, a professor of Suzhou University of Science and Technology, Ph.D., engages in functional analysis, convex geometry analysis and mathematical morphology.
Supported by:
Supported by the NNSF of China(11271282)

摘要/Abstract

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∈Kⁿd_BM(C,△)≤n + 2, where d_BM(.,.) denotes the Banach-Mazur distance, △ denotes an n-dimensional simplex and Kⁿ denotes the class of n-dimensional convex sets in Rⁿ.

关键词: Banach-Mazur distance, simplex, convex body

Abstract: 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∈Kⁿd_BM(C,△)≤n + 2, where d_BM(.,.) denotes the Banach-Mazur distance, △ denotes an n-dimensional simplex and Kⁿ denotes the class of n-dimensional convex sets in Rⁿ.

Key words: Banach-Mazur distance, simplex, convex body

中图分类号:

O184

国起. 一般凸体与单形间Banach-Mazur距离估计的一种简单方法[J]. 数学季刊, 2012, 27(4): 504-508.

GUO Qi. A Simple Approach to Estimating the Banach-Mazur Distance between Simplex and Convex Bodies[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(4): 504-508.

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