Quasi-convex subsets in Alexandrov spaces with lower curvature bound

Xiaole SU; Hongwei SUN; Yusheng WANG

doi:10.1007/s11464-021-0955-0

Front. Math. China ›› 2022, Vol. 17 ›› Issue (6) : 1063 -1082. DOI: 10.1007/s11464-021-0955-0

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Quasi-convex subsets in Alexandrov spaces with lower curvature bound

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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.

Keywords

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

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

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