Applications of Toponogov's comparison theorems for open triangles

zbMath1275.53037arXiv1102.4156MaRDI QIDQ2393587

Kei-Ichi Kondo, Minoru Tanaka

Publication date: 8 August 2013

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

Full work available at URL: https://arxiv.org/abs/1102.4156

zbMATH Keywords

geodesic triangleradial curvatureRiemannian comparison

Mathematics Subject Classification ID

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

Cites Work

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• Toponogov comparison theorem for open triangles
• Ricci curvature, geodesics and some geometric properties of Riemannian manifolds with boundary
• A generalized sphere theorem
• The dimension of a cut locus on a smooth Riemannian manifold
• Compactification and maximal diameter theorem for noncompact manifolds with radial curvature bounded below
• Comparison geometry referred to warped product models
• On complete open manifolds of positive curvature
• On the structure of complete manifolds of nonnegative curvature
• Generalized space forms
• Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. II
• Decomposition of Cut Loci
• CONVEX SETS IN RIEMANNIAN SPACES OF NON-NEGATIVE CURVATURE
• 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
• A Sard theorem for the distance function

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