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].
Capogna, L., Citti, G., Le Donne, E., Ottazzi, A. (2019). Conformality and Q-harmonicity in sub-Riemannian manifolds. JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES, 122, 67-124 [10.1016/j.matpur.2017.12.006].
Conformality and Q-harmonicity in sub-Riemannian manifolds
Capogna, Luca;Citti, Giovanna;Le Donne, Enrico;
2019
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].| File | Dimensione | Formato | |
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1-QC-Subriemannian-update@for@CVGMT.pdf
Open Access dal 02/03/2021
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