Stationary radial centers and symmetry of convex polytopes

Abstract

We investigate centers of a body (the closure of a bounded open set) in R m defined as maximum points of potentials. In particular, we study centers defined by the Riesz potential and by Poisson's integral. These centers, in general, depend on parameters and move with respect to the parameters. We give a necessary and sufficient condition for the existence of a center independent of a parameter.