具有非负Ricci曲率和次大体积增长的完备流形

摘要

本文研究了具有非负Ricci曲率和次大体积增长的完备黎曼流形的拓扑结构问题.利用Toponogov型比较定理及临界点理论,获得了流形具有有限拓扑型的结果,推广了H.Zhan和Z.Shen的定理,并且还证明了该流形的基本群是有限生成的.%In this paper,we study the topology of complete Riemannian manifolds with nonnegative Ricci curvature and sub-large volume growth.By Toponogov's comparison theorems and critical point theory,we obtain some results on finite topological type,which improve the theorem proved by H.Zhan and Z.Shen.We also prove that such a manifold has a finitely generated fundamental group.