Geometriae Dedicata

, Volume 159, Issue 1, pp 169–184 | Cite as

Erratic behavior of CAT(0) geodesics under G-equivariant quasi-isometries

Original Paper


We show that, given any connected, compact space \({Z \subset \mathbb{R}^n}\), there exists a group G acting geometrically on two CAT(0) spaces X and Y, a G-equivariant quasi-isometry \({f\colon X\rightarrow Y}\), and a geodesic ray c in X such that the closure of f (c), intersected with \({\partial Y}\), is homeomorphic to Z. This characterizes all homeomorphism types of “geodesic boundary images” that arise in this manner.


Hadamard space Geodesic ray Geometric group theory 

Mathematics Subject Classification (2000)

20F65 20F67 20F69 


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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Department of MathematicsRutgers UniversityPiscatawayUSA

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