In this talk, using the local Ricci flow, we prove the 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
was studied by Wan-Xiong Shi in 1990s, who required a point-wise bound of
curvature tensors. As a corollary of our main theorem, we get the short-time existence part of Shis theorem in this more general context.