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math.DG2022
A proof of Toponogov's theorem in Alexandrov geometry
Shengqi Hu, Xiaole Su, Yusheng Wang
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…
math.DG2021
New definitions of Alexandrov space and applications
Shengqi Hu, Xiaole Su, Yusheng Wang
In this paper we show that, in the definition of Alexandrov spaces with lower or upper curvature bound, the original conditions can be replaced with much weaker ones. For the purpo…