Lower bounds on Ricci curvature and the almost rigidity of warped products

@article{Cheeger1996LowerBO,
  title={Lower bounds on Ricci curvature and the almost rigidity of warped products},
  author={J. Cheeger and T. Colding},
  journal={Annals of Mathematics},
  year={1996},
  volume={144},
  pages={189-237}
}
The basic rigidity theorems for manifolds of nonnegative or positive Ricci curvature are the "volume cone implies metric cone" theorem, the maximal diameter theorem, [Cg], and the splitting theorem, [CG]. Each asserts that if a certain geometric quantity (volume or diameter) is as large as possible relative to the pertinent lower bound on Ricci curvature, then the metric on the manifold in question is a warped product metric of a particular type. In this paper we provide quantitative… Expand

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