An estimate of the centroid Banach-Mazur distance between planar convex bodies

Abstract

We consider the variant of the Banach-Mazur distance ${\delta }_{BM}^{\mathrm{cen}}(C,D)$ of two convex bodies $C,D$ of $E^d$ with the additional requirement that the centroids of them coincide. We prove that ${\delta }_{BM}^{\mathrm{cen}}(C,D)\le \frac{69}{17}$ for every $C,D$ of $E^2$.

6 pages, 2 figures. arXiv admin note: text overlap with arXiv:2202.01815