Conformal and CR mappings on Carnot groups

Michael G. Cowling, Ji Li, Alessandro Ottazzi, Qingyan Wu

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    We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and affine in each component. As examples, we consider free groups on two generators, and show that these admit very simple polynomial embeddings in CN that induce their CR structure.
    Original languageEnglish
    Pages (from-to)67-81
    Number of pages15
    JournalProceedings of the American Mathematical Society, Series B
    Publication statusPublished - 17 Jun 2020

    Bibliographical note

    Copyright the Author(s) 2020. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


    • Carnot groups
    • CR mappings
    • quasiconformal mappings
    • conformal mappings


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