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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 thatconverges to the energy double integral, with a rate of convergence dependingon the geodesic ball discrepancy. This generalizes a known result for thesphere.

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