Conformality and Q-harmonicity in Carnot Groups

Authors

Luca Capogna, University of ArkansasFollow
Michael Cowling, UNSW Sydney

Document Type

Article

Publication Date

12-1-2006

Publication Title

Duke Mathematical Journal

Abstract

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.

Volume

135

Issue

3

First Page

455

Last Page

479

DOI

10.1215/S0012-7094-06-13532-9

ISSN

00127094

Comments

Archived as published.

Recommended Citation

Capogna, Luca and Cowling, Michael, "Conformality and Q-harmonicity in Carnot Groups" (2006). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/143