A note on the Ricci flow on noncompact manifolds

Abstract

Let $(M^3,g_0)$ be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with injectivity radius bounded away from zero. Suppose that the scalar curvature $R(x)\to 0$ as $x\to \infty$. Then the Ricci flow with initial data $(M^3,g_0)$ has a long time solution. This extends a recent result of Ma and Zhu. We also have a higher dimensional version, and we reprove a K$\ddot{a}$hler analogy due to Chau, Tam and Yu.

3 pages, a new theorem added

References in corpus (2)

• Pseudolocality for the Ricci flow and applications
• Nonsingular Ricci flow on a noncompact manifold in dimension three