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Conformality And Q-Harmonicity In Sub-Riemannian Manifolds, Luca Capogna, Giovanna Citti, Enrico Le Donne, Alessandro Ottazzi

Mathematics Sciences: Faculty Publications

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].