Estimates for Diameter and Width for the Isoperimetrix in Minkowski Geometry

• Date: 2006
• Main Author: Diskant, V. I.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України 2006
• Subjects: isoperimetrix; Minkowski geometry; convex body; diameter; width
• Online Access: https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1048
• Journal Title: Journal of Mathematical Physics, Analysis, Geometry

The following estimates are obtained for the diameter$D_B(I)$ and the width $\Delta_B(I)$ of isoperimetrix in Minkowski space $M^n$$$\displaystyle\frac{4v_{n-1}}{nv_n}\le \Delta_B(I)\le D_B(I)\le \displaystyle\frac{4v_{n-1}}{v_n},$$ where $v_n$ is a volume of the unit ball in $n$-dimensional Euclide...