Conformality and Q-harmonicity in sub-Riemannian manifolds
Abstract
We establish regularity of conformal maps between sub-Riemannian manifolds from regularity of Q-harmonic functions, and in particular we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth in all contact sub-Riemannian manifolds. Together with the recent results in [15], our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains [29].
Main Authors
Format
Articles
Research article
Published
2019
Series
Subjects
Publication in research information system
Publisher
Elsevier Masson
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201901171227Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
0021-7824
DOI
https://doi.org/10.1016/j.matpur.2017.12.006
Language
English
Published in
Journal de Mathematiques Pures et Appliquees
Citation
- Capogna, L., Citti, G., Le Donne, E., & Ottazzi, A. (2019). Conformality and Q-harmonicity in sub-Riemannian manifolds. Journal de Mathematiques Pures et Appliquees, 122, 67-124. https://doi.org/10.1016/j.matpur.2017.12.006
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Funder(s)
European Commission
Academy of Finland
Funding program(s)
EU:n 7. puiteohjelma (FP7)
Akatemiatutkija, SA
FP7 (EU's 7th Framework Programme)
Academy Research Fellow, AoF
Additional information about funding
Partially funded by NSF awards DMS 1449143 and DMS 1503683.2. Partially funded by the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007–2013/ under REA grant agreement No. 607643 and by the European Unions Horizon 2020 research programme, Marie Skłodowska-Curie grant agreement No. 777822. 3. Supported by the Academy of Finland, project No. 288501.4. Partially supported by the Australian Research Council, project No. DP140100531.
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