Toponogov comparison theorem for open triangles

Kei Kondo, Minoru Tanaka

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)363-396
Number of pages34
JournalTohoku Mathematical Journal
Volume63
Issue number3
DOIs
Publication statusPublished - Sep 2011
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint

Dive into the research topics of 'Toponogov comparison theorem for open triangles'. Together they form a unique fingerprint.

Cite this