A PROOF OF TOPONOGOV?S THEOREM IN ALEXANDROV GEOMETRY

This note aims to give an elementary proof for Toponogov's the-orem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in geodesic variations.

Automated summary

This note presents an elementary proof for Toponogov's theorem in Alexandrov geometry with a lower curvature bound. The proof is based on the idea that in Riemannian geometry, sectional curvature can be manifested in geodesic variations.