Fuchsian Groups, Quasiconformal Groups, and Conical Limit Sets
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- by Peter W. Jones and Lesley A. Ward PDF
- Trans. Amer. Math. Soc. 352 (2000), 311-362 Request permission
Abstract:
We construct examples showing that the normalized Lebesgue measure of the conical limit set of a uniformly quasiconformal group acting discontinuously on the disc may take any value between zero and one. This is in contrast to the cases of Fuchsian groups acting on the disc, conformal groups acting discontinuously on the ball in dimension three or higher, uniformly quasiconformal groups acting discontinuously on the ball in dimension three or higher, and discrete groups of biholomorphic mappings acting on the ball in several complex dimensions. In these cases the normalized Lebesgue measure is either zero or one.References
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Additional Information
- Peter W. Jones
- Affiliation: Department of Mathematics, Yale University, New Haven, Connecticut 06520–8283
- Email: jones@math.yale.edu
- Lesley A. Ward
- Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005–1892, and MSRI, 1000 Centennial Drive, Berkeley, California 94720–5070
- Address at time of publication: Department of Mathematics, Harvey Mudd College, Claremont, California 91711
- MR Author ID: 614761
- Email: ward@math.hmc.edu
- Received by editor(s): February 1, 1996
- Received by editor(s) in revised form: May 13, 1997
- Published electronically: September 9, 1999
- Additional Notes: Partially supported by NSF grant #DMS-92-13595.
Research at MSRI supported in part by NSF grant #DMS-90-22140. - © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 311-362
- MSC (1991): Primary 30C62, 30F35, 20H10
- DOI: https://doi.org/10.1090/S0002-9947-99-02118-2
- MathSciNet review: 1458326