ON MINMAX AND MAXMIN INEQUALITIES FOR CENTERED CONVEX BODIES

One of the challenging problems from the geometry of (normed or) Minkowki spaces is the question of whether the unit ball must be an ellipsoid if it is a solution of the corresponding isoperimetric problem. The inner and outer radii of the unit ball with respect to the corresponding isoperimetrix (represented in terms of cross-section measures) will be used to establish a result on this problem for a specific measure. Some new minmax and maxmin inequalities for centered convex bodies will also be established.