Quasi-convex subsets and the farthest direction in Alexandrov spaces with lower curvature bound

TL;DR

This paper investigates quasi-convex subsets in Alexandrov spaces with lower curvature bounds, providing new insights and properties that deepen understanding of their geometric structure.

Contribution

It introduces new theoretical insights and properties of quasi-convex subsets in Alexandrov spaces, expanding prior foundational work.

Findings

New theorems and corollaries on quasi-convex subsets

Enhanced understanding of their geometric properties

Applications to broader Alexandrov space theory

Abstract

This paper aims to give a further study on quasi-convex subsets in Alexandrov spaces with lower curvature bound which are introduced in [SSW]. We first provide new insights on quasi-convex subsets (Theorem A and Corollary C), and then as applications of them we explore more properties of quasi-convex subsets.