Optimal Green energy points on the circles in d-space

Abstract

We give two precise estimates for the Green energy of a discrete charge, concentrated in the points on the circles, with respect to the concentric rotation domain in the d-dimensional Euclidean space, d > 2.The proof is based on the application of a dissymmetrization, extremal metrics approach and an asymptotic formula for the condenser capacities in the case when some of its plates contract to given points.