Volume growth and the topology of manifolds with nonnegative Ricci curvature

DOI10.1007/s12220-010-9125-4zbMath1200.53043arXiv0712.0827OpenAlexW2147011092WikidataQ125585597 ScholiaQ125585597MaRDI QIDQ980407

Michael Munn

Publication date: 29 June 2010

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

Full work available at URL: https://arxiv.org/abs/0712.0827

zbMATH Keywords

volume growthhomotopy groupsnonnegative Ricci curvature

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (7)

Metric measure spaces supporting Gagliardo-Nirenberg inequalities: volume non-collapsing and rigidities ⋮ Universal curvature identities. II. ⋮ Second-order Sobolev inequalities on a class of Riemannian manifolds with nonnegative Ricci curvature ⋮ Alexandrov spaces with large volume growth ⋮ Volume growth and the topology of manifolds with nonnegative Ricci curvature ⋮ Volume growth and the topology of pointed Gromov-Hausdorff limits ⋮ Elliptic differential inclusions on non-compact Riemannian manifolds

Cites Work

• A finiteness theorem for Ricci curvature in dimension three
• On the topology of complete manifolds of non-negative Ricci curvature
• Volume growth and the topology of manifolds with nonnegative Ricci curvature
• On the structure of spaces with Ricci curvature bounded below. I
• Noncollapsing examples with positive Ricci curvature and infinite topological type
• Friedmann cosmology and almost isotropy
• Large time behavior of the heat equation on complete manifolds with non- negative Ricci curvature
• On Complete Manifolds With Nonnegative Ricci Curvature
• Manifolds of Positive Ricci Curvature with Almost Maximal Volume
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