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

Abstract

We prove that if $K,L\subset {\mathbb{R}}^2$ are convex bodies such that $L$ is symmetric and the Banach-Mazur distance between $K$ and $L$ is equal to $2$, then $K$ is a triangle.

arXiv comment17 pages, 13 figures

References in corpus (2)

• On the Banach-Mazur Distance between the Cube and the Crosspolytope
• On Banach-Mazur distance between planar convex bodies