Hausdorff dimension distribution of quasiconformal mappings on the Heisenberg group
- Cite this article as:
- Balogh, Z.M. J. Anal. Math. (2001) 83: 289. doi:10.1007/BF02790265
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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.