A rigidity phenomenon on Riemannian manifolds with reverse volume pinching

DOI10.1007/s10455-007-9094-4zbMath1152.53028OpenAlexW2008694222WikidataQ115384679 ScholiaQ115384679MaRDI QIDQ934641

Yuliang Wen, Peihe Wang

Publication date: 30 July 2008

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-007-9094-4

zbMATH Keywords

harmonic radiusHausdorff convergencedifferentiable sphere theoremvolume comparison theoremharmonic coordinate

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Rigidity results (53C24) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

A differentiable sphere theorem with positive Ricci curvature and reverse volume pinching ⋮ A rigidity phenomenon on Riemannian manifolds with reverse excess pinching

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Estimate of the first eigenvalue for a compact Riemann manifold
• Manifolds near the boundary of existence
• On the spectral gap for compact manifolds
• Convergence and rigidity of manifolds under Ricci curvature bounds
• A differentiable sphere theorem on manifolds with reverse volume pinching
• Oscillation criteria for self-adjoint second-order differential systems and Principal sectional curvatures
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• \(C^ \alpha\)-compactness for manifolds with Ricci curvature and injectivity radius bounded below
• Rigidity of manifolds with large volume
• Rigidity and sphere theorem for manifolds with positive Ricci curvature
• A note on pinching sphere theorem.
• Lower bound estimates of the first eigenvalue for compact manifolds with positive Ricci curvature
• Hard and soft packing radius theorems
• A gap phenomenon on Riemannian manifolds with reverse volume pinching
• Smooth diameter and eigenvalue rigidity in positive Ricci curvature
• A Sphere Theorem for Manifolds of Positive Ricci Curvature
• A Sphere Theorem for Reverse Volume Pinching on Even-Dimensional Manifolds
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu