IUMJ

Title: Quasi-circles through prescribed points

Authors: John Mackay

Issue: Volume 63 (2014), Issue 2, 403-417

Abstract:

We show that in an $L$-annularly linearly connected, $N$-doubling, complete metric space, any $n$ points lie on a $\lambda$-quasi-circle, where $\lambda$ depends only on $L, N$, and $n$. This implies that, for example, if $G$ is a hyperbolic group that does not split over any virtually cyclic subgroup, then any geodesic line in $G$ lies in a quasi-isometrically embedded copy of $\mathbb{H}^2$.