Tohoku Mathematical Journal
2011
September
SECOND SERIES VOL. 63, NO. 3

Tohoku Math. J.
63 (2011), 363-396

Title TOPONOGOV COMPARISON THEOREM FOR OPEN TRIANGLES

Author Kei Kondo and Minoru Tanaka

(Received June 1, 2010, revised January 31, 2011)
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.

2000 Mathematics Subject Classification. Primary 53C21; Secondary 53C22.
Key words and phrases. Cut locus, focal locus, open triangle, radial curvature, Riemannian manifold with boundary, Toponogov's comparison theorem.

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