Cheeger, Jeff; Colding, Tobias H. On the structure of spaces with Ricci curvature bounded below. I. (English) Zbl 0902.53034 J. Differ. Geom. 46, No. 3, 406-480 (1997). The authors investigate the structure of spaces which are pointed Gromov-Hausdorff limits of sequences of complete, connected Riemannian manifolds whose Ricci curvatures have a definite lower bound. Sometimes they also assume a lower volume bound. The presented results, most of which were announced and proved in earlier papers of the authors [see J. Cheeger and T. H. Colding, Ann. Math., II. Ser. 144, 189-237 (1996; Zbl 0865.53037)], are applications of the “almost rigidity” theorems for manifolds of almost nonnegative Ricci curvature. Applying metrics of doubly warped product type, the authors construct a number of examples of spaces which are Gromov-Hausdorff limits of sequences of pointed Riemannian manifolds of positive Ricci curvature. Reviewer: M.Hotloś (Wrocław) Cited in 27 ReviewsCited in 346 Documents MSC: 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions Keywords:bounded Ricci curvature; Gromov-Hausdorff limit; doubly warped product Citations:Zbl 0865.53037 PDFBibTeX XMLCite \textit{J. Cheeger} and \textit{T. H. Colding}, J. Differ. Geom. 46, No. 3, 406--480 (1997; Zbl 0902.53034) Full Text: DOI