Toponogov comparison theorem for open triangles

Details Toponogov comparison theorem for open triangles Toponogov comparison theorem for open triangles

2009-05-20

arxiv.org/abs/0905.3236v4

Tohoku Mathematical Journal, vol. 63 (2011), no. 3, pp.363-396

Mathematics

Differential Geometry

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

Scientific paper

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).

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