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Conformal Geometry and Dynamics

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Global contact and quasiconformal mappings of Carnot groups


Authors: Michael G. Cowling and Alessandro Ottazzi
Journal: Conform. Geom. Dyn. 19 (2015), 221-239
MSC (2010): Primary 30L10; Secondary 57S20, 35R03, 53C23
DOI: https://doi.org/10.1090/ecgd/282
Published electronically: September 29, 2015
MathSciNet review: 3402499
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Abstract: We show that globally defined quasiconformal mappings of rigid Carnot groups are affine, but that globally defined contact mappings of rigid Carnot groups need not be quasiconformal, and a fortiori not affine.


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Additional Information

Michael G. Cowling
Affiliation: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia

Alessandro Ottazzi
Affiliation: CIRM, Fondazione Bruno Kessler, Via Sommarive 15, I-38123 Trento, Italy
Address at time of publication: School of Mathematics and Statistics, University of New South Wales, UNSW Sydney 2052, Australia

DOI: https://doi.org/10.1090/ecgd/282
Keywords: Carnot groups, quasiconformal mappings, contact mappings
Received by editor(s): April 14, 2015
Received by editor(s) in revised form: September 7, 2015
Published electronically: September 29, 2015
Additional Notes: Both authors thank the Australian Research Council for support (DP140100531), and the referee for reading the paper very carefully and helping to improve it. The second named author partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)
Article copyright: © Copyright 2015 American Mathematical Society