Journal de Mathématiques Pures et Appliquées
We prove the equivalence of several natural notions of conformal maps between sub-Riemannian manifolds. Our main contribution is in the setting of those manifolds that support a suitable regularity theory for subelliptic p-Laplacian operators. For such manifolds we prove a Liouville-type theorem, i.e., 1-quasiconformal maps are smooth. In particular, we prove that contact manifolds support the suitable regularity. The main new technical tools are a sub-Riemannian version of p-harmonic coordinates and a technique of propagation of regularity from horizontal layers.
Capogna, L., Citti, G., Le Donne, E., & Ottazzi, A. (2017). Conformality and Q-harmonicity in sub-Riemannian manifolds. Journal de Mathématiques Pures et Appliquées. https://doi.org/10.1016/j.matpur.2017.12.006