We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound,which include not only all closed convex subsets without boundary but also all extremal subsets.Moreover,we explore several essential p...We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound,which include not only all closed convex subsets without boundary but also all extremal subsets.Moreover,we explore several essential properties of such kind of subsets including a generalized Liberman theorem.It turns out that the quasi-convex subset is a nice and fundamental concept to illustrate the similarities and differences between Riemannian manifolds and Alexandrov spaces with lower curvature bound.展开更多
基金supported in part by the National Natural Science Foundation of China(Grant No.11971057)Beijing Natural Science Foundation(No.Z190003).
文摘We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound,which include not only all closed convex subsets without boundary but also all extremal subsets.Moreover,we explore several essential properties of such kind of subsets including a generalized Liberman theorem.It turns out that the quasi-convex subset is a nice and fundamental concept to illustrate the similarities and differences between Riemannian manifolds and Alexandrov spaces with lower curvature bound.
