Quasi-Circles Through Prescribed Points

We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a λ-quasi-circle, where λ 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 i...

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Bibliographic Details
Published in:Indiana University mathematics journal 2014-01, Vol.63 (2), p.403-417
Main Author: Mackay, John M.
Format: Article
Language:English
Subjects:
Circles
Closed curves
College mathematics
Combinatorics
Geodesy
Geometric planes
Mathematical theorems
Topological theorems
Topology
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Summary:We show that in an L-annularly linearly connected, N-doubling, complete metric space, any n points lie on a λ-quasi-circle, where λ 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 ℍ2.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2014.63.5211