Geodesic
A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the Heisenberg group
Alex D. Austin1 ; Jeremy T. Tyson2
1 Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, U.S.A.
2 Department of Mathematics University of Illinois at Urbana-Champaign 1409 West Green St. Urbana, IL 61801, U.S.A.
Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 217-228 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm7193-3-2017
Keywords: proof infty regularity smooth conformal mappings sub riemannian heisenberg group proof avoids nonlinear potential theory relies only hypoellipticity rmander operators quasiconformal flows approach inspired prior work sarvas liu

Alex D. Austin 1 ; Jeremy T. Tyson 2

1 Department of Mathematics University of California, Los Angeles Box 951555 Los Angeles, CA 90095-1555, U.S.A.
2 Department of Mathematics University of Illinois at Urbana-Champaign 1409 West Green St. Urbana, IL 61801, U.S.A. 
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     title = {A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the {Heisenberg} group},
     journal = {Colloquium Mathematicum},
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Alex D. Austin; Jeremy T. Tyson. A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the Heisenberg group. Colloquium Mathematicum, Tome 150 (2017) no. 2, pp. 217-228. doi: 10.4064/cm7193-3-2017

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