-stable Fuchsian groups.
Some homeomorphisms of the sphere conformal off a curve.
On a theorem of Beardon and Maskit.
Quasiconformal mappings which increase dimension.
BiLipschitz approximations of quasiconformal maps.
Locally minimal sets for conformal dimension.
On conformal dilatation in space.
Conformal welding of rectifiable curves.
Non-rectifiable limit sets of dimension one.
We construct quasiconformal deformations of convergence type Fuchsian groups such that the resulting limit set is a Jordan curve of Hausdorff dimension 1, but having tangents almost nowhere. It is known that no divergence type group has such a deformation. The main tools in this construction are (1) a characterization of tangent points in terms of Peter Jones' beta's, (2) a result of Stephen Semmes that gives a Carleson type condition on a Beltrami coefficient which implies rectifiability and (3)...
Quasiconformal mappings of Y-pieces.
In this paper we construct quasiconformal mappings between Y-pieces so that the corresponding Beltrami coefficient has exponential decay away from the boundary. These maps are used in a companion paper to construct quasiFuchsian groups whose limit sets are non-rectifiable curves of dimension 1.
An indestructible Blaschke product in the little Bloch space.
The little Bloch space, B, is the space of all holomorphic functions f on the unit disk such that lim lf'(z)l (1- lzl) = 0. Finite Blaschke products are clearly in B, but examples of infinite products in B are more difficult to obtain (there are now several constructions due to Sarason, Stephenson and the author, among others). Stephenson has asked whether B contains an infinite, indestructible Blaschke product, i.e., a Blaschke product B so that (B(z) - a)/(1 - âB(z)), is also a Blaschke product...
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