Geometriae Dedicata

, Volume 162, Issue 1, pp 337–344 | Cite as

On the fundamental group of Riemannian manifolds with nonnegative Ricci curvature

Original Paper


In 1968 Milnor conjectured that the fundamental group of any complete Riemannian manifold with nonnegative Ricci curvature is finitely generated. In this paper we obtain two results concerning Milnor’s conjecture. We first prove that the generators of fundamental group can be chosen so that it has at most logarithmic growth. Secondly we prove that the conjecture is true if additional the volume growth satisfies certain condition.


Riemannian manifold Ricci curvature Fundamental group Finitely generated 

Mathematics Subject Classification

53C23 53B40 58B20 


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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsMinjiang UniversityFuzhouChina

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