Toponogov comparison theorem for open triangles
Differential Geometry
2011-09-14 v4
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).
Keywords
Cite
@article{arxiv.0905.3236,
title = {Toponogov comparison theorem for open triangles},
author = {Kei Kondo and Minoru Tanaka},
journal= {arXiv preprint arXiv:0905.3236},
year = {2011}
}
Comments
This version 4 (36 pages, no figures) is a version to appear in Tohoku Mathematical Journal