Duke Mathematical Journal

Conformality and $Q$-harmonicity in Carnot groups

Luca Capogna and Michael Cowling

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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

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Duke Math. J. Volume 135, Number 3 (2006), 455-479.

First available in Project Euclid: 10 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations 35H20: Subelliptic equations
Secondary: 22E25: Nilpotent and solvable Lie groups


Capogna, Luca; Cowling, Michael. Conformality and Q -harmonicity in Carnot groups. Duke Mathematical Journal 135 (2006), no. 3, 455--479. doi:10.1215/S0012-7094-06-13532-9. http://projecteuclid.org/euclid.dmj/1163170199.

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