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.

Creator

• Citti, Giovanna
• Le Donne, Enrico
• Capogna, Luca
• Ottazzi, Alessandro

Keyword

• Harmonic Coordinates
• Regularity for P-Harmonic Functions
• Quasi-Conformal Maps
• Subelliptic Pde
• Liouville Theorem
• Sub-Riemannian Geometry

Date created

• 12/11/17

Resource type

• Article

Extent

• 67 pages

Source

• https://doi.org/10.1016/j.matpur.2017.12.006

Rights statement

• In Copyright

Last modified

• 2020-09-22