Frontiers of Mathematics in China >

2022 , Vol. 17 >Issue 6: 1063 - 1082

DOI: https://doi.org/10.1007/s11464-021-0955-0

RESEARCH ARTICLE

Quasi-convex subsets in Alexandrov spaces with lower curvature bound

  • Xiaole SU 1 ,
  • Hongwei SUN 2 ,
  • Yusheng WANG , 1
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  • 1. School of Mathematical Sciences (and Key Laboratory Mathematics and Complex Systems, Ministry of Education, China), Beijing Normal University, Beijing 100875, China
  • 2. School of Mathematics Sciences, Capital Normal University, Beijing 100037, China

Received date: 24 Nov 2020

Accepted date: 12 Jul 2021

Copyright

2022 Higher Education Press
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Abstract

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.

Key words： Quasi-convex subset; Alexandrov space; extremal subset; quasigeodesic

Cite this article

Xiaole SU , Hongwei SUN , Yusheng WANG . Quasi-convex subsets in Alexandrov spaces with lower curvature bound[J]. Frontiers of Mathematics in China, 2022 , 17(6) : 1063 -1082 . DOI: 10.1007/s11464-021-0955-0

References

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