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

Voir la notice de l'article

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. 
@article{10_4064_cm7193_3_2017,
     author = {Alex D. Austin and Jeremy T. Tyson},
     title = {A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the {Heisenberg} group},
     journal = {Colloquium Mathematicum},
     pages = {217--228},
     year = {2017},
     volume = {150},
     number = {2},
     doi = {10.4064/cm7193-3-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm7193-3-2017/}
}
TY  - JOUR
AU  - Alex D. Austin
AU  - Jeremy T. Tyson
TI  - A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the Heisenberg group
JO  - Colloquium Mathematicum
PY  - 2017
SP  - 217
EP  - 228
VL  - 150
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm7193-3-2017/
DO  - 10.4064/cm7193-3-2017
LA  - en
ID  - 10_4064_cm7193_3_2017
ER  - 
%0 Journal Article
%A Alex D. Austin
%A Jeremy T. Tyson
%T A new proof of the $C^\infty $ regularity of $C^2$ conformal mappings on the Heisenberg group
%J Colloquium Mathematicum
%D 2017
%P 217-228
%V 150
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/cm7193-3-2017/
%R 10.4064/cm7193-3-2017
%G en
%F 10_4064_cm7193_3_2017
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

Cité par Sources :