Conformality and $Q$ -harmonicity in Carnot groups
Capogna, Luca ; Cowling, Michael
Duke Math. J., Tome 131 (2006) no. 1, p. 455-479 / Harvested from Project Euclid
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We show that if $f$ is a $1$ -quasiconformal map defined on an open subset of a Carnot group $G$ , then composition with $f$ preserves $Q$ -harmonic functions. We combine this with a regularity theorem for $Q$ -harmonic functions and an algebraic regularity theorem for maps between Carnot groups to show that $f$ is smooth. We give some applications to the study of rigidity
Publié le : 2006-12-01
Classification:  30C65,  35H20,  22E25 
@article{1163170199,
     author = {Capogna, Luca and Cowling, Michael},
     title = {Conformality and $Q$ -harmonicity in Carnot groups},
     journal = {Duke Math. J.},
     volume = {131},
     number = {1},
     year = {2006},
     pages = { 455-479},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163170199}
}

Capogna, Luca; Cowling, Michael. Conformality and $Q$ -harmonicity in Carnot groups. Duke Math. J., Tome 131 (2006) no. 1, pp.  455-479. http://gdmltest.u-ga.fr/item/1163170199/