  In this paper, we give the first detailed proof of the short-time existence
of Deane Yang's local Ricci flow. Then using the local Ricci flow, we prove
short-time existence of the Ricci flow on noncompact manifolds, whose Ricci
curvature has global lower bound and sectional curvature has only local average
integral bound. The short-time existence of the Ricci flow on noncompact
manifolds with bounded curvature was studied by Wan-Xiong Shi in 1990s. As a
corollary of our main theorem, we get the short-time existence part of Shi's
theorem in this more general context.
