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arXiv · 1512.09165

Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings

Tomasz Adamowicz·Ben Warhurst
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Abstract

We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending Näkki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the Loewner property. Using prime ends we show the counterpart of Caratheodory's extension theorem for quasiconformal mappings, the Koebe theorem on arcwise limits, the Lindelöf theorem for principal points and the Tsuji theorem.

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Tomasz Adamowicz, Ben Warhurst. 2015-12-30. Prime ends in the Heisenberg group $\mathbb{H}_{1}$ and the boundary behavior of quasiconformal mappings. https://arxiv.org/abs/1512.09165

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