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math.DG2018
A Schur-Toponogov theorem in Riemannian geometry & a new proof of Toponogov's theorem in Alexandrov geometry
Yusheng Wang
In the paper, we give a Schur-Toponogov theorem in Riemannian geometry, which not only generalizes Schur's and Toponogov's theorem but also indicates their relation. Inspired by it…
math.MG2018
The Soul Conjecture in Alexandrov Geometry in dimension 4
Xiaochun Rong, Yusheng Wang
In this paper, we prove the Soul Conjecture in Alexandrov geometry in dimension , i.e. if is a complete non-compact -dimensional Alexandrov space of non-negative curvatur…