  We discuss a set of relations, set in the form of results, conjectures and
problems, between the L^{2}-norm of the Ricci curvature of a 3-manifold, the
scalar curvature and the volume radius. We illustrate the scope of these
relations with potential applications to the Einstein Constant Mean Curvature
flow (or GR seen as a geometric flow of constant mean curvature), but we
believe the framework has it own geometric interest.
