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

Autor:	Adamowicz, Tomasz, Warhurst, Ben
Rok vydání:	2015
Předmět:	Mathematics - Metric Geometry 30D40 (Primary) 30L10 30C65 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.09165 Zobrazit plný text záznamu View this record from Arxiv