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

• Date: 2024
• Main Author: Lassak, Marek
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2024
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7428
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...