Toponogov comparison theorem for open triangles

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)363-396
Number of pages34
JournalTohoku Mathematical Journal
Issue number3
Publication statusPublished - Sept 2011
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics


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