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Conformality and Q-harmonicity in Carnot groups

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Dec 2006 United States, Australia Publisher:Duke University PressJournal:Duke Mathematical Journal, volume 135 (issn: 0012-7094, Copyright policy )
Authors: Capogna, Luca; Cowling, Michael;

doi: 10.1215/s0012-7094-06-13532-9

handle: 1959.4/42656

Conformality and Q-harmonicity in Carnot groups

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

Countries
United States, Australia
Related Organizations
Keywords

22E25, 35H20, Mathematics, 30C65

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    		 31
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Average
    influence
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
31
Average
Top 10%
Average
Green