Local convexity in CAT(κ)-spaces

Abstract

Heinrich Tietze has shown that for a closed connected subset of euclidean space being convex is a local property. We generalize this to CAT(0)-spaces and locally compact CAT(κ) spaces. As an application we give a construction of certain convex sets in euclidean buildings.

13 pages, 2 figures; v2 added references

Cited by in corpus (2)

• Quasiconvex Subgroups of F_m x Z^n are Convex
• Convexity is a local property in $CAT(\kappa )$ spaces