A new proof of the $C^{\infty }$ regularity of $C^2$ conformal mappings on the Heisenberg group

Alex D. Austin, Jeremy T. Tyson

We give a new proof for the $C^{\infty }$ regularity of $C^2$ smooth conformal mappings of the sub-Riemannian Heisenberg group. Our proof avoids any use of nonlinear potential theory…