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 Math. J. 135 (2006), no. 3, 455--479. doi:10.1215/S0012-7094-06-13532-9. https://projecteuclid.org/euclid.dmj/1163170199

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