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].
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 in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
1-QC-Subriemannian-update@for@CVGMT.pdf
Open Access dal 02/03/2021
Tipo:
Postprint
Licenza:
Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione
1.18 MB
Formato
Adobe PDF
|
1.18 MB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
