On Banach-Mazur distance between planar convex bodies

Abstract

Upper estimates of the diameter and the radius of the family of all planar convex bodies with respect to the Banach-Mazur distance are obtained. Namely, it is shown that the diameter does not exceed $\frac{19-\sqrt{73}}{4}\approx 2.614$, which improves the previously known bound of $3$, and that the radius does not exceed $\frac{117}{70}\approx 1.671$.

References in corpus (1)

• Distances between non--symmetric convex bodies and the $M{M}^{\ast }$-estimate

Cited by in corpus (1)

• Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane