TOPONOGOV COMPARISON THEOREM FOR OPEN TRIANGLES

KEI KONDO; MINORU TANAKA

doi:10.2748/tmj/1318338947

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

TOPONOGOV COMPARISON THEOREM FOR OPEN TRIANGLES

KEI KONDO, MINORU TANAKA

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Keywords: Cut locus, focal locus, open triangle, radial curvature, Riemannian manifold with boundary, Toponogov's comparison theorem

JOURNAL FREE ACCESS

2011 Volume 63 Issue 3 Pages 363-396

DOI https://doi.org/10.2748/tmj/1318338947

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Abstract

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.

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