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 |
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Pages (from-to) | 363-396 |
Number of pages | 34 |
Journal | Tohoku Mathematical Journal |
Volume | 63 |
Issue number | 3 |
DOIs | |
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)