A1 Journal article (refereed)
A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group (2020)

Adamowicz, T., Fässler, K., & Warhurst, B. (2020). A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group. Annali di Matematica Pura ed Applicata, 199(1), 147-186. https://doi.org/10.1007/s10231-019-00871-8

JYU authors or editors

Publication details

All authors or editors: Adamowicz, Tomasz; Fässler, Katrin; Warhurst, Ben

Journal or series: Annali di Matematica Pura ed Applicata

ISSN: 0373-3114

eISSN: 1618-1891

Publication year: 2020

Volume: 199

Issue number: 1

Pages range: 147-186

Publisher: Springer

Publication country: Germany

Publication language: English

DOI: https://doi.org/10.1007/s10231-019-00871-8

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67879

Publication is parallel published: https://arxiv.org/abs/1707.02832

Web address where publication is available: https://arxiv.org/abs/1707.02832

Abstract

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 integrals of the average derivative and the operator norm of the horizontal differential, as well as the study of quasiconformal densities and metrics in domains in H1. The theorems are discussed for the sub-Riemannian and the Korányi distances. This extends results due to Astala–Gehring, Astala–Koskela, Koskela and Bonk–Koskela–Rohde.

Free keywords: Koebe distortion theorem; Quasiconformal mapping; Heisenberg group

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1