  In this paper we construct a Ricci de Turck flow on any incomplete Riemannian
manifold with bounded curvature. The central property of the flow is that it
stays uniformly equivalent to the initial incomplete Riemannian metric, and in
that sense preserves any given initial singularity structure. Together with the
corresponding result by Shi for complete manifolds, this gives that any
(complete or incomplete) manifold of bounded curvature can be evolved by the
Ricci de Turck flow for a short time.
