Annales Academiæ Scientiarum Fennicæ
Volumen 43, 2018, 631-668
Polish Academy of Sciences, Institute of Mathematics
ul. Sniadeckich 8, 00-656 Warsaw, Poland; T.Adamowicz 'at' impan.pl
University of Warsaw, Institute of Mathematics
ul. Banacha 2, 02-097 Warsaw, Poland; B.Warhurst 'at' mimuw.edu.pl
Abstract. We investigate prime ends in the Heisenberg group H1, extending Näakki'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 Carathéodory's extension theorem for quasiconformal mappings, the Koebe theorem on arcwise limits, the Lindelöf theorem for principal points, and the Tsuji theorem.
2010 Mathematics Subject Classification: Primary 30D40; Secondary 30L10, 30C65.
Key words: Capacity, Carnot group, collared, extension, finitely connected at the boundary, Heisenberg group, Koebe, Lie algebra, Lie group, Lindelöf, p-modulus, prime end, quasiconformal, sub-Riemannian, Tsuji.
Reference to this article: T. Adamowicz and B. Warhurst: Prime ends in the Heisenberg group H1 and the boundary behavior of quasiconformal mappings. Ann. Acad. Sci. Fenn. Math. 43 (2018), 631-668.
Full document as PDF file
Copyright © 2018 by Academia Scientiarum Fennica