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Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group

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Abstract

We construct quasiconformal mappings on the Heisenberg group which change the Hausdorff dimension of Cantor-type sets in an arbitrary fashion. On the other hand, we give examples of subsets of the Heisenberg group whose Hausdorff dimension cannot be lowered by any quasiconformal mapping. For a general set of a certain Hausdorff dimension we obtain estimates of the Hausdorff dimension of the image set in terms of the magnitude of the quasiconformal distortion.

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  1. Mathematisches Institut, Universität Bern, Sidlerstr. 5, CH-3012, Bern, Switzerland

    Zoltán M. Balogh

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  1. Zoltán M. Balogh
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Balogh, Z.M. Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group. J. Anal. Math. 83, 289–312 (2001). https://doi.org/10.1007/BF02790265

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  • DOI: https://doi.org/10.1007/BF02790265

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