Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 203-213

CONFORMAL MAPS OF CARNOT GROUPS

Michael G. Cowling and Alessandro Ottazzi

University of New South Wales, School of Mathematics and Statistics
UNSW Sydney 2052, Australia; m.cowling 'at' unsw.edu.au

Fondazione Bruno Kessler, Centro Internazionale per la Ricerca Matematica
Via Sommarive 15, I-38123 Trento, Italia; ottazzi 'at' fbk.eu

Abstract. If f is a conformal mapping defined on a connected open subset Ω of a Carnot group G, then either f is the composition of a translation, a dilation and an isometry, or G is the nilpotent Iwasawa component of a real rank 1 simple Lie group S, and f arises from the action of S on G, viewed as an open subset of S/P, where P is a parabolic subgroup of G and NP is open and dense in S.

2010 Mathematics Subject Classification: Primary: 57S20; Secondary 30L10, 35R03, 53C23.

Key words: Carnot groups, conformal mappings, Tanaka prolongation.

Reference to this article: M. G. Cowling and A. Ottazzi: Conformal maps of Carnot groups. Ann. Acad. Sci. Fenn. Math. 40 (2015), 203-213.

Full document as PDF file

doi:10.5186/aasfm.2015.4008