Stationary radial centers and symmetry of convex polytopes
We investigate centers of a body (the closure of a bounded open set) in $\mathbb R ^m$ 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 vary with the parameters. We give a necessary and sufficient condition for the existence of a center independent of a parameter.