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Manifolds with lower Ricci and L1-Sectional curvature control
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 2, April 2005
- pp. 459-469
- 10.1353/ajm.2005.0013
- Article
- Additional Information
Suppose that a sequence of Riemannian manifolds with Ricci curvature ≥ -k2 converges to a Gromov-Hausdorff limit X. We show that if the amount of sectional curvature below K of the limiting manifolds approaches 0 in a suitable L1-sense, then X is an Alexandrov space of curvature ≥ K. As applications we present several generalizations of classical theorems.