  Given a closed submanifold, or a compact regular domain, in euclidean space,
we consider the Riesz energy defined as the double integral of some power of
the distance between pairs of points. When this integral diverges, we compare
two different regularization techniques (Hadamard's finite part and analytic
continuation), and show that they give essentially the same result. We prove
that some of these energies are invariant under Moebius transformations, thus
giving a generalization to higher dimensions of the Moebius energy of knots.
