Journal of the
Korean Mathematical Society JKMS

In this paper we derive some basic inequalities connecting the Minkowski measure of symmetry, the Minkowski symmetral and the Banach-Mazur distance. We then explore the geometric contents of these inequalities and shed light on the structure of the quotient $\cb/{\rm Aff}$ of the space of convex bodies modulo the affine transformations.

Keywords: convex body, Minkowski measure of symmetry, Minkowski symmetral, Banach-Mazur distance

MSC numbers: 52A20, 52A38