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arXiv · 1210.5119

Quasi-circles through prescribed points

John M. Mackay
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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.

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John M. Mackay. 2013-10-26. Quasi-circles through prescribed points. https://doi.org/10.1512/iumj.2014.63.5211

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