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

Volume 150 / 2017

Alex D. Austin, Jeremy T. Tyson Colloquium Mathematicum 150 (2017), 217-228 MSC: Primary 30L10; Secondary 30C65, 53C17, 35J70. DOI: 10.4064/cm7193-3-2017 Published online: 28 July 2017

Abstract

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.

Authors

  • Alex D. AustinDepartment of Mathematics
    University of California, Los Angeles
    Box 951555
    Los Angeles, CA 90095-1555, U.S.A.
    e-mail
  • Jeremy T. TysonDepartment of Mathematics
    University of Illinois at Urbana-Champaign
    1409 West Green St.
    Urbana, IL 61801, U.S.A.
    e-mail

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