Journal des Mathematiques Pures et Appliquees
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 , our work yields a new proof of the smoothness of boundary extensions of biholomorphims between strictly pseudoconvex smooth domains .
Harmonic coordinates, Liouville Theorem, Quasi-conformal maps, Regularity for p-harmonic functions, Sub-Riemannian geometry, Subelliptic PDE
Capogna, Luca; Citti, Giovanna; Le Donne, Enrico; and Ottazzi, Alessandro, "Conformality and Q-harmonicity in Sub-Riemannian Manifolds" (2019). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.