A proof of Toponogov's theorem in Alexandrov geometry

Published 28 Mar 2022 in math.DG and math.MG | (2203.14626v1)

Abstract: This paper aims to give an elementary proof for Toponogov's theorem 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 the second variation formula.

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