In this paper we prove that if M is a compact, hyperbolizable 3manifold, which is not a handlebody, then the Hausdorff dimension of the limit set is continuous in the strong topology on the space of… (More)

A hyperbolic manifold M is K-quasiconformally homogeneous (0 ≤ K < ∞) if for all x, y ∈ M there exists a K-quasiconformal selfmapping of M that maps x to y. Here, quasiconformal mappings are… (More)

Knowledge of factors affecting sample integrity is vital to make informed judgements on the validity of results. However, the information available for sample stability is incomplete, confusing and… (More)

Let M be a compact 3-manifold whose interior admits a complete hyperbolic structure. We let Λ(M) be the supremum of λ0(N) where N varies over all hyperbolic 3-manifolds homeomorphic to the interior… (More)

We show that any closed hyperbolic surface admitting a conformal automorphism with “many” fixed points is uniformly quasiconformally homogeneous, with constant uniformly bounded away from 1. In… (More)

We show that a discrete, quasiconformal group preserving Hn has the property that its exponent of convergence and the Hausdorff dimension of its limit set detect the existence of a non-empty regular… (More)

We show that there exists a universal constant Kc so that every K-strongly quasiconformally homogeneous hyperbolic surface X (not equal to H2) has the property that K > Kc > 1. The constant Kc is the… (More)

We extend the part of Patterson-Sullivan theory to discrete quasiconformal groups that relates the exponent of convergence of the Poincaré series to the Hausdorff dimension of the limit set. In doing… (More)