Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry - Diskant, V. I. (Журнал математичної фізики, аналізу, геометрії, 2006)
The following estimates are obtained for the diameter$D_B(I)$ and the width $Δ_B(I)$ of isoperimetrix in Minkowski space $M^n$ $$\displaystyle\frac{4v_{n-1}}{nv_n}\le Δ_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclidean space $R^n.$ The first inequality turns into equality for a bicone, the last inequality turns into equality for a cube. Mathematics Subject Classification 2000: 52A38, 52A40.