The maximum relative diameter for multi-rotationally symmetric planar convex bodies

Abstract

In this work we study the maximum relative diameter functional dM in the class of multi-rotationally symmetric planar convex bodies. A given set C of this class is k-rotationally symmetric for k 2 {k1, . . . , kn} N, and so it is natural to consider the standard ki-partition Pki associated to C (which is a minimizing ki-partition for dM when ki > 3) and the corresponding value dM(Pki ). We establish the relation among these values, characterizing the particular sets for which all these values coincide.