Minimal Energy Asymptotics in the “Harmonic Series” Case

Abstract

This chapter deals with the asymptotic behavior of the value of the minimal Riesz d-energy on compact subsets of d-dimensional \(C^1\) manifolds in \(\mathbb R^p\), \(d\le p\). The weak\(^*\)-limit distribution of sequences of energy minimizing configurations and lower estimates of their minimal pairwise separation can be also found here. Finally, a class of sequences of asymptotically d-energy minimizing configurations is constructed for sets of positive d-dimensional Lebesgue measure.