Stationary radial centers and symmetry of convex polytopes
Volume 159 / 2020
Colloquium Mathematicum 159 (2020), 91-106
MSC: Primary 35B38, 52B15; Secondary 52A39, 52A10.
DOI: 10.4064/cm7712-11-2018
Published online: 10 October 2019
Abstract
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.
