A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the Heisenberg group
Tom 150 / 2017
Colloquium Mathematicum 150 (2017), 217-228 MSC: Primary 30L10; Secondary 30C65, 53C17, 35J70. DOI: 10.4064/cm7193-3-2017 Opublikowany online: 28 July 2017
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 Hörmander operators and quasiconformal flows. This approach is inspired by prior work of Sarvas and Liu.