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We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki's construction for collared domains in Euclidean spaces. The corresponding class of domains is defined via uniform domains and the… Click to show full abstract
We investigate prime ends in the Heisenberg group $\mathbb{H}_{1}$ extending N\"akki'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 Lindel\"of theorem for principal points and the Tsuji theorem.
Keywords:
prime ends;
heisenberg group;
group boundary;
quasiconformal mappings;
ends heisenberg
Journal Title: Annales Academiae Scientiarum Fennicae Mathematica
Year Published: 2018
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Journal Title: Annales Academiae Scientiarum Fennicae Mathematica
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!