中文摘要：

设（M^3，90）是非紧三维Riemann流形，其Ricci曲率非负，单射半径有正的下界，且当x→∞时数量曲率R（x）→0。则以（M^3，go）为初始值的Ricci流在M^3×[0，∞）上有长期解。这推广了马和朱最近的一个结果．在高维情形我们也有相应的结果，并且我们给Chau，Tam和Yu在Ktihler情形的类似定理一个新的证明。

英文摘要：

Let （M^3, go） be a complete noncompact Riemannian 3-manifold with nonnegative Ricci curvature and with iajectivity radius bounded away from zero. Suppose that the scalar curvature R（x）→ 0 as x → ∞. Then the Ricci flow with initial data （M^3, go） has a long time solution on M^3 × [0, ∞）. This extends a recent result of Ma and Zhu. We also have a higher dimensional version, and we reprove a Kahler analogue due to Chau, Tam and Yu.