Estimation of the centroid Banach–Mazur distance between planar convex bodies

Marek Lassak

doi:10.3842/umzh.v76i5.7428

Marek Lassak University of Science and Technology, Bydgoszcz, Poland

DOI: https://doi.org/10.3842/umzh.v76i5.7428

Keywords: Banach-Mazur distance, centroid Banach-Mazur distance, convex body, centroid, affine-regular hexagon

Abstract

UDC 514.18

We consider a version of the Banach–Mazur distance $\delta_{BM}^{\rm cen} (C, D)$ between two convex bodies $C$ and $D$ from $E^d$ with an additional requirement that their centroids coincide. We prove that $\delta_{BM}^{\rm cen} (C, D) \leq \dfrac{69}{17}$ for any two convex bodies $C$ and $D$ in $E^2.$

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