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Inventiones mathematicae

, Volume 193, Issue 2, pp 367–375 | Cite as

3-Manifolds with nonnegative Ricci curvature

  • Gang LiuEmail author
Article

Abstract

For a complete noncompact 3-manifold with nonnegative Ricci curvature, we prove that either it is diffeomorphic to ℝ3 or the universal cover splits. This confirms Milnor’s conjecture in dimension 3.

Keywords

Universal Cover Ricci Curvature Ricci Flow Local Isometry Nonnegative Ricci Curvature 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The author would like to thank Professors Richard Schoen, Jiaping Wang, Shing-Tung Yau for their interests in this note. He also thanks Chenxu He for informing him the paper [3].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MinnesotaMinneapolisUSA

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