Quasi-convex subsets in Alexandrov spaces with lower curvature bound

被引：0

作者：

Su, Xiaole ^{[1
,2
]}

Sun, Hongwei ^{[3
]}

Wang, Yusheng ^{[1
,2
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Beijing Normal Univ, Minist Educ, Key Lab Math & Complex Syst, Beijing 100875, Peoples R China

[3] Capital Normal Univ, Sch Math Sci, Beijing 100037, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2021年 / 17卷 / 06期

基金：

中国国家自然科学基金; 北京市自然科学基金;

关键词：

Quasi-convex subset; Alexandrov space; extremal subset; quasigeodesic;

D O I：

10.1007/s11464-021-0955-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1063 / 1082

页数：20

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