Nonsingular Ricci flow on a noncompact manifold in dimension three

This is the authors' abstract. We don't add key points for this paper.

We consider the Ricci flow ∂/∂ tg=-2Ric on the 3-dimensional complete noncompact manifold $(M,g(0))$ with non-negative curvature operator, i.e., Rm≥ 0, |Rm(p)|→ 0, ~as ~d(o,p)→ 0. We prove that the Ricci flow on such a manifold is nonsingular in any finite time.