Non-rectifiable limit sets of dimension one.
type: Item
instance of: scholarly article
title: Non-rectifiable limit sets of dimension one.
zbMATH Open document ID: 1064.30046
DOI: 10.4171/RMI/331
author: Christopher J. Bishop
published in: Revista Matemática Iberoamericana
publication date: 2003-09-25T00:00:00Z
full work available at URL: https://eudml.org/doc/39698
review text: The author considers and constructs 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. He answers the question, asked by \textit{M. Zinsmeisters} and \textit{K. Astala} [C. R. Acad. Sci., Paris, Sér. I 311, 301--306 (1990; Zbl 0709.30039)], that whether there are quasi-Fuchsian groups whose limit set are not locally rectifiable, but still have dimension 1, by showing that there are many such groups.
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 1931494
reviewed by: Ismail Naci Cangül
MaRDI profile type: Publication
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OpenAlex ID: W2048791508
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description: scientific article; zbMATH DE number 1931494