Deformation of C⁰ Riemannian metrics in the direction of their Ricci curvature

The purpose of this paper is to evolve non-smooth Riemannian metric tensors by the dual Ricci-Harmonic map flow. This flow is equivalent (up to a diffeomorphism) to the Ricci flow. One application will be the evolution of metrics which arise in the study of spaces whose curvature is bounded from above and below in the sense of Aleksandrov, and whose curvature operator (in dimension three Ricci curvature) is non-negative. We show that such metrics may always be deformed to a smooth metric having the same properties in a strong sense.