## Non-rectifiable limit sets of dimension one.(English)Zbl 1064.30046

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 M. Zinsmeisters and 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.

### MSC:

 30F60 Teichmüller theory for Riemann surfaces

Zbl 0709.30039
Full Text:

### References:

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