Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II

DOI10.1090/S0002-9947-2010-05031-7zbMath1225.53034arXiv0901.4019MaRDI QIDQ3065740

Minoru Tanaka, Kei-Ichi Kondo

Publication date: 6 January 2011

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4019

zbMATH Keywords

comparison theoremcontrol topologyradial curvatures

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global Riemannian geometry, including pinching (53C20)

Related Items

Approximations of Lipschitz maps via Ehresmann fibrations and Reeb's sphere theorem for Lipschitz functions ⋮ Applications of Toponogov's comparison theorems for open triangles ⋮ Generalized von Mangoldt surfaces of revolution and asymmetric two-spheres of revolution with simple cut locus structure ⋮ Modification of the sector theorem of Kondo-Tanaka ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I ⋮ The Alexandrov-Toponogov comparison theorem for radial curvature ⋮ A sphere theorem for radial curvature ⋮ Toponogov comparison theorem for open triangles ⋮ Sufficient conditions for open manifolds to be diffeomorphic to Euclidean spaces ⋮ Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. III ⋮ On sufficient conditions to extend Huber's finite connectivity theorem to higher dimensions ⋮ Necessary and sufficient conditions for a triangle comparison theorem ⋮ The topology of an open manifold with radial curvature bounded from below by a model surface with finite total curvature and examples of model surfaces

Uses Software

• Loki

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