2015/12/30 by Adamowicz, Tomasz, Warhurst, Ben
#30C65 (Secondary) #30D40 (Primary) #30L10 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1512.09165
We investigate prime ends in the Heisenberg group ℍ1 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.