Nonsingular Ricci flow on a noncompact manifold in dimension three

Abstract

We consider the Ricci flow $\frac{\partial }{\partial t}g=-2Ric$ on the 3-dimensional complete noncompact manifold $(M,g(0))$ with non-negative curvature operator, i.e., $Rm\ge 0,|Rm(p)|\to 0,asd(o,p)\to 0.$ We prove that the Ricci flow on such a manifold is nonsingular in any finite time.

6 pages

References in corpus (1)

• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

Cited by in corpus (1)

• A note on the Ricci flow on noncompact manifolds