Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (4): 504-508.

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

  

  1. 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)

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 supC∈KndBM(C,△)≤n + 2, where dBM(.,.) 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

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