A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group

Adamowicz, Tomasz; Fässler, Katrin; Warhurst, Ben

doi:10.1007/s10231-019-00871-8

dc.contributor.author	Adamowicz, Tomasz
dc.contributor.author	Fässler, Katrin
dc.contributor.author	Warhurst, Ben
dc.date.accessioned	2020-02-19T09:33:17Z
dc.date.available	2020-02-19T09:33:17Z
dc.date.issued	2020
dc.identifier.citation	Adamowicz, T., Fässler, K., & Warhurst, B. (2020). A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group. <i>Annali di Matematica Pura ed Applicata</i>, <i>199</i>(1), 147-186. <a href="https://doi.org/10.1007/s10231-019-00871-8" target="_blank">https://doi.org/10.1007/s10231-019-00871-8</a>
dc.identifier.other	CONVID_30874132
dc.identifier.other	TUTKAID_81537
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/67879
dc.description.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.	en
dc.format.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Springer
dc.relation.ispartofseries	Annali di Matematica Pura ed Applicata
dc.rights	CC BY 4.0
dc.subject.other	Kvasikonformikuvaus
dc.subject.other	Heisenbergin ryhmä
dc.subject.other	Koebe distortion theorem
dc.subject.other	Quasiconformal mapping
dc.subject.other	Heisenberg group
dc.title	A Koebe distortion theorem for quasiconformal mappings in the Heisenberg group
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-202002182091
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2020-02-18T07:15:12Z
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	147-186
dc.relation.issn	0373-3114
dc.relation.numberinseries	1
dc.relation.volume	199
dc.type.version	publishedVersion
dc.rights.copyright	© 2019 the Author(s)
dc.rights.accesslevel	openAccess	fi
dc.format.content	fulltext
dc.rights.url	https://creativecommons.org/licenses/by/4.0/
dc.relation.doi	10.1007/s10231-019-00871-8
jyx.fundinginformation	Open access funding provided by University of Jyväskylä (JYU).
dc.type.okm	A1