Stationary radial centers and characterization of convex polyhedrons

TL;DR

This paper studies special centers of convex bodies defined via potential functions, providing conditions for when such centers are independent of parameters, advancing understanding of geometric potential theory.

Contribution

It offers a necessary and sufficient condition for the existence of parameter-independent centers defined by Riesz potential and Poisson's integral.

Findings

Centers depend on parameters in general

Condition for parameter-independent centers is established

Advances geometric potential theory understanding

Abstract

We investigate centers of a body (the closure of a bounded open set) 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.