Toponogov comparison theorem for open triangles

Abstract

Dedicated to Professor Gromoll: The aim of our article is to generalize the Toponogov comparison theorem to a complete Riemannian manifold with smooth convex boundary. A geodesic triangle will be replaced by an open (geodesic) triangle standing on the boundary of the manifold, and a model surface will be replaced by the universal covering surface of a cylinder of revolution with totally geodesic boundary. Applications of our theorem are found in our article "Applications of Toponogov's comparison theorems for open triangles" (arXiv:1102.4156).

This version 4 (36 pages, no figures) is a version to appear in Tohoku Mathematical Journal

References in corpus (1)

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

Cited by in corpus (2)

• Total curvatures of model surfaces control topology of complete open manifolds with radial curvature bounded below. I
• Applications of Toponogov's comparison theorems for open triangles