Small excess and Ricci curvature

DOI10.1007/BF02921313zbMath0742.53013WikidataQ125877557 ScholiaQ125877557MaRDI QIDQ1177618

Peter V Petersen

Publication date: 26 June 1992

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

Ricci curvaturemetric spaceinjectivity radiusexcessbounded geometrytwisted spherediameter-sphere-theorem

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (8)

Manifolds tightly covered by two metric balls ⋮ An excess sphere theorem ⋮ Smooth diameter and eigenvalue rigidity in positive Ricci curvature ⋮ On Riemannian manifolds with \(\epsilon\)-maximal diameter and bounded curvature ⋮ Closed manifolds with small excess. ⋮ Manifolds with small excess and bounded curvature ⋮ Rigidity of manifolds with large volume ⋮ Differentiable sphere theorems for Ricci curvature

Cites Work

• Diameter, volume, and topology for positive Ricci curvature
• On manifold of positive Ricci curvature with large diameter
• Metrics of positive Ricci curvature with large diameter
• The topology of certain Riemannian manifolds with positive Ricci curvature
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• Eigenvalue comparison theorems and its geometric applications
• A generalized sphere theorem
• On the smoothness of isometries
• Riemannian manifolds with positive mean curvature
• A Sphere Theorem for Manifolds of Positive Ricci Curvature
• A Diameter Pinching Sphere Theorem for Positive Ricci Curvature
• Convex functions on complete noncompact manifolds : differentiable structure
• Convergence of Riemannian 3-Manifolds Under a Ricci Curvature Bound
• A Pinching Theorem for Homotopy Spheres

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