论文标题
Alexandrov空间中的准凸出子集具有较低的曲率结合
Quasi-convex subsets in Alexandrov spaces with lower curvature bound
论文作者
论文摘要
在本文中，我们在具有较低曲率结合的Alxandrov空间中介绍了准串联子集，其中不仅包括所有没有边界的闭合凸子集，而且包括所有极端亚集。此外，我们探讨了这种种类的几种基本特性，包括广义的自由主义者定理。事实证明，准凸出子集是一个不错的基本概念，可以说明Riemannian流形和具有较低曲率结合的Alxandrov空间之间的相似性和差异。
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 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 Alxandrov spaces with lower curvature bound.
