Toponogov comparison theorem for open triangles

Kei Kondo; Minoru Tanaka

doi:10.2748/tmj/1318338947

Toponogov comparison theorem for open triangles

Kei Kondo, Minoru Tanaka

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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.

Original language	English
Pages (from-to)	363-396
Number of pages	34
Journal	Tohoku Mathematical Journal
Volume	63
Issue number	3
DOIs	https://doi.org/10.2748/tmj/1318338947
Publication status	Published - Sep 2011
Externally published	Yes

Keywords

Cut locus
Focal locus
Open triangle
Radial curvature
Riemannian manifold with boundary
Toponogov's comparison theorem

ASJC Scopus subject areas

Mathematics(all)

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KW - Riemannian manifold with boundary

KW - Toponogov's comparison theorem

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