Quasi-circles through prescribed points
arXiv:1210.5119 · doi:10.1512/iumj.2014.63.5211
Abstract
We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a K-quasi-circle, where K depends only on L, N and n. This implies, for example, that 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 the hyperbolic plane.
v1: 15 pages, 2 figures; v2: 16 pages, 2 figures. Minor changes. Version accepted by IUMJ