Ricci flow from singular spaces with bounded curvature

Abstract

We show the existence of a solution to the Ricci flow with a compact length space of bounded curvature, i.e., a space that has curvature bounded above and below in the sense of Alexandrov, as its initial condition. We show that this flow converges in the $C^{1,\alpha}$-sense to a $C^{1,\alpha}$-continuous Riemannian manifold which is isometric to the original metric space. Moreover, we prove that the flow is uniquely determined by the initial condition, up to isometry.