Metric curvature, convergence, and topological finiteness

DOI10.1215/S0012-7094-92-06602-6zbMath0770.53033OpenAlexW1974571618MaRDI QIDQ1196381

Conrad P. Plaut

Publication date: 14 December 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-92-06602-6

zbMATH Keywords

injectivity radiusgeodesic spacesmoothness assumptionsCheeger finiteness theoremGromov convergence theorem

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items

Spaces of Wald curvature bounded below, Disconnectedness of sublevel sets of some Riemannian functionals, Metric Curvatures Revisited: A Brief Overview, Geometrizing Infinite Dimensional Locally Compact Groups, Unnamed Item, Conjugate points in length spaces, Manifolds of almost nonnegative curvature, Metric pinching of locally symmetric spaces

Cites Work

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• Almost Riemannian spaces
• Smoothness of the metric of spaces with two-sided bounded Aleksandrov curvature
• Manifolds near the boundary of existence
• A finiteness theorem for metric spaces
• Lipschitz convergence of Riemannian manifolds
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Collapsing and pinching under a lower curvature bound
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• Correction to ``Metric pinching of locally symmetric spaces
• Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds.
• Bounded curvature closure of the set of compact Riemannian manifolds
• A convergence theorem for Riemannian manifolds and some applications
• Finiteness Theorems for Riemannian Manifolds