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.
Citation
Kei Kondo. Minoru Tanaka. "Toponogov comparison theorem for open triangles." Tohoku Math. J. (2) 63 (3) 363 - 396, 2011. https://doi.org/10.2748/tmj/1318338947
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