A new proof of the C^infty regularity of C² conformal mappings on the Heisenberg group

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 and relies only on hypoellipticity of H\"ormander operators and quasiconformal flows. This approach is inspired by prior work of Sarvas and Liu.