6 papers
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…
Quasi-convex subsets and the farthest direction in Alexandrov spaces with lower curvature bound
Xiaole Su, Hongwei Sun, Yusheng Wang
This paper aims to give a further study on quasi-convex subsets in Alexandrov spaces with lower curvature bound which are introduced in [SSW]. We first provide new insights on quas…
Quasi-convex subsets in Alexandrov spaces with lower curvature bound
Xiaole Su, Hongwei Sun, Yusheng Wang
In this paper, we introduce quasi-convex subsets in Alxandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary but also all extr…
Pythagorean Theorem & curvature with lower or upper bound
Xiaole Su, Hongwei Sun, Yusheng Wang
In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).
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…
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…