A Volume Comparison Theorem for Manifolds with Asymptotically Nonnegative Curvature and its Applications

DOI10.2307/2374996zbMath0953.53027OpenAlexW2312693314MaRDI QIDQ4303465

Shun-Hui Zhu

Publication date: 4 October 1994

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2374996

zbMATH Keywords

topological rigidityasymptotically nonnegative Ricci curvatureasymptotically nonnegative curvatureBishop-Gromov volume comparison theorem

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20)

Related Items (14)

Volume comparison theorems in Finsler spacetimes ⋮ On complete manifolds supporting a weighted Sobolev type inequality ⋮ The Caffarelli-Kohn-Nirenberg inequality on metric measure spaces ⋮ Open manifolds with asymptotically nonnegative Ricci curvature and large volume growth ⋮ The log-Sobolev inequality for a submanifold in manifolds with asymptotic non-negative intermediate Ricci curvature ⋮ The logarithmic Sobolev inequality for a submanifold in manifolds with asymptotically nonnegative sectional curvature ⋮ Comparison geometry referred to warped product models ⋮ A theorem of DoCarmo-Zhou type: oscillations and estimates for the first eigenvalue of the \(p\)-Laplacian ⋮ Hardy type inequalities on complete Riemannian manifolds ⋮ Manifolds with asymptotically nonnegative minimal radial curvature ⋮ A volume comparison estimate with radially symmetric Ricci curvature lower bound and its applications ⋮ Sobolev type inequalities on Riemannian manifolds ⋮ Lower volume estimates and Sobolev inequalities ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II

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