Li, Nan; Wang, Feng Lipschitz-volume rigidity on limit spaces with Ricci curvature bounded from below. (English) Zbl 1295.53034 Differ. Geom. Appl. 35, 50-55 (2014). Summary: We prove a Lipschitz-Volume rigidity theorem for the non-collapsed Gromov-Hausdorff limits of manifolds with Ricci curvature bounded from below. This is a counterpart of the Lipschitz-Volume rigidity in Alexandrov geometry. Cited in 4 Documents MSC: 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C45 Global surface theory (convex surfaces à la A. D. Aleksandrov) 53C24 Rigidity results Keywords:Ricci curvature; volume; rigidity; Lipschitz map; Gromov-Hausdorff convergence; comparison; Cheeger-Colding PDFBibTeX XMLCite \textit{N. Li} and \textit{F. Wang}, Differ. Geom. Appl. 35, 50--55 (2014; Zbl 1295.53034) Full Text: DOI arXiv References: [1] Burago, Y.; Gromov, M.; Perel’man, G., A.D. Alexandrov spaces with curvature bounded below, Usp. Mat. Nauk. Usp. Mat. Nauk, Russ. Math. Surv., 47, 2, 1-58 (1992), translation in · Zbl 0802.53018 [2] Bessières, L.; Besson, G.; Courtois, G.; Gallot, S., Differentiable rigidity under Ricci curvature lower bound, Duke Math. J., 161, 1, 29-67 (2012) · Zbl 1250.53033 [3] Cheeger, Jeff; Colding, Tobias, On the structure of spaces with Ricci curvature bounded below I, J. Differ. Geom., 45, 406-480 (1997) · Zbl 0902.53034 [4] Cheeger, Jeff; Colding, Tobias, On the structure of spaces with Ricci curvature bounded below II, J. Differ. Geom., 54, 12-35 (2000) · Zbl 1027.53042 [5] Colding, Tobias, Shape of manifolds with positive Ricci curvature, Invent. Math., 124, 175-191 (1996) · Zbl 0871.53027 [6] Colding, Tobias, Large manifolds with positive Ricci curvature, Invent. Math., 124, 193-214 (1996) · Zbl 0871.53028 [7] Colding, Tobias, Ricci curvature and volume convergence, Ann. Math., 145, 477-501 (1997) · Zbl 0879.53030 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.