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

Alex D. Austin, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review


We give a new proof for the C regularity of C2 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.

Original languageEnglish (US)
Pages (from-to)217-228
Number of pages12
JournalColloquium Mathematicum
Issue number2
StatePublished - 2017


  • Conformal mapping
  • Heisenberg group
  • Korányi–Reimann flow

ASJC Scopus subject areas

  • Mathematics(all)


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