On the separation distance of minimal Green energy points on compact Riemannian manifolds

Abstract

In this article we study point configurations minimizing the discrete energy on a compact Riemannian manifold, where the energy kernel is taken to be the Green's function for the Laplacian. We show that every point in a minimizing configuration lies inside an open set called harmonic ball where no other point can enter, and that the minimum distance between any two distinct points has the optimal asymptotic order. We compute explicit bounds for the minimum distance in the case of Compact Rank One Symmetric Spaces.