  It is shown that the supports of measures minimizing weakly repulsive
energies on Riemannian manifolds with sectional curvature bounded below do not
have concentration points. This extends the results of Bj\"orck and Carrillo,
Figalli, and Patacchini for such energies on the Euclidean space, and
complements the results about the discreteness of minimizers of the geodesic
Riesz energy on the sphere by Bilyk, Dai, and Matzke.
