The splitting theorem for manifolds of nonnegative Ricci curvature

1971/09/01 by Jeff Cheeger, Detlef Gromoll · 11 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Comparison theorem #Curvature #Curvature of Riemannian manifolds #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows #Geometry #Mathematical analysis #Mathematics #Pure mathematics #Ricci curvature #Ricci-flat manifold #Scalar curvature #Sectional curvature

paper · pdf · doi:10.4310/jdg/1214430220

crossref issued 1971/09/01 · crossref published 1971/09/01 · crossref published-print 1971/09/01 · openalex publication_date 1971/09/01 · crossref created 2017/03/16 · crossref deposited 2021/05/09 · openalex created_date 2025/10/10 · crossref indexed 2026/07/22 · openalex updated_date 2026/07/23

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• Convergence and rigidity of manifolds under Ricci curvature bounds
• Splitting theorems on complete manifolds with Bakry-Émery curvature
• The Liouville theorem for p-harmonic functions and quasiminimizers with finite energy
• On the escape rate of geodesic loops in an open manifold with nonnegative Ricci curvature
• A Spectral Splitting Theorem for the N-Bakry Émery Ricci tensor
• Collapsing Geometry with Ricci Curvature Bounded Below and Ricci Flow Smoothing
• New restrictions on the topology of extreme black holes
• A Course in Metric Geometry
• Local estimate of fundamental groups
• Topology and 𝜖–regularity theorems on collapsed manifolds with Ricci curvature bounds
• Splitting theorem [wikipedia]