# A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group

@article{Adamowicz2019AKD, title={A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group}, author={Tomasz Adamowicz and Katrin F{\"a}ssler and Ben Warhurst}, journal={Annali di Matematica Pura ed Applicata (1923 -)}, year={2019}, volume={199}, pages={147-186} }

We prove a Koebe distortion theorem for the average derivative of a quasiconformal mapping between domains in the sub-Riemannian Heisenberg group $${\mathbb {H}}^{1}$$ H 1 . Several auxiliary properties of quasiconformal mappings between subdomains of $${\mathbb {H}}^{1}$$ H 1 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 integrals of the average derivative and the operator… Expand

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