Revista Matemática Iberoamericana

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Volume 18, Issue 3, 2002, pp. 627–652
DOI: 10.4171/RMI/330

Published online: 2002-12-31

Quasiconformal mappings of $Y$-pieces

Christopher J. Bishop[1]

(1) SUNY at Stony Brook, USA

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.

Keywords: Hausdorff dimension, quasi-Fuchsian groups, quasiconformal deformation, critical exponent, convex core

Bishop Christopher: Quasiconformal mappings of $Y$-pieces. Rev. Mat. Iberoam. 18 (2002), 627-652. doi: 10.4171/RMI/330