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    Université de Fribourg

    A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group

    Adamowicz, Tomasz ; Fässler, Katrin ; Warhurst, Ben

    In: Annali di Matematica Pura ed Applicata (1923 -), 2020, vol. 199, no. 1, p. 147–186

    We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group H1. Several auxiliary properties of quasiconformal mappings between subdomains of H1 are proven, including BMO estimates for the logarithm of the Jacobian. Applications of the Koebe theorem include diameter bounds for images of curves, comparison of...