Journal
ANNALS OF MATHEMATICS
Volume 154, Issue 1, Pages 205-217Publisher
Princeton Univ, Dept Mathematics
DOI: 10.2307/3062115
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We show that every deformation of a divergence-type Fuchsian group has a limit set which is either a circle or has dimension strictly larger than 1. This is known to be false for all convergence-type groups, and hence solves Bowen's problem in the general case. The proof uses a theorem of Dennis Sullivans about convex hulls in hyperbolic 3-space and we give a new, simpler proof of this result as well.
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