Local convexity in CAT(κ)-spaces

2012/11/08 by Kai-Uwe Bux, Kai‐Uwe Bux, Bux, Kai-Uwe +2 · 1 citation
Computer Science · Mathematics · #51F99 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Variational Analysis #Point processes and geometric inequalities #math.MG #msc:51F99

paper · pdf · doi:10.48550/arxiv.1211.1871

13 pages, 2 figures; v2 added references

openalex publication_date 2012/11/08 · arxiv created 2014/09/23 · arxiv updated 2014/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Quasiconvex Subgroups of F_m x Zⁿ are Convex

Cited by

• The Hirsch conjecture holds for normal flag complexes

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