Discrepancy, separation and Riesz energy of finite point sets on compact connected Riemannian manifolds

Abstract

On a smooth compact connected d-dimensional Riemannian manifold M, if 0 < s < d then an asymptotically equidistributed sequence of finite subsets of M that is also well-separated yields a sequence of Riesz s-energies that converges to the energy double integral, with a rate of convergence depending on the geodesic ball discrepancy. This generalizes a known result for the sphere. Show more