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dc.contributor.authorIkonen, Toni
dc.date.accessioned2021-11-10T11:17:29Z
dc.date.available2021-11-10T11:17:29Z
dc.date.issued2021
dc.identifier.citationIkonen, T. (2021). Quasiconformal Jordan Domains. <i>Analysis and Geometry in Metric Spaces</i>, <i>9</i>(1), 167-185. <a href="https://doi.org/10.1515/agms-2020-0127" target="_blank">https://doi.org/10.1515/agms-2020-0127</a>
dc.identifier.otherCONVID_101837523
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/78585
dc.description.abstractWe extend the classical Carathéodory extension theorem to quasiconformal Jordan domains (Y,dY). We say that a metric space (Y,dY) is a quasiconformal Jordan domain if the completion Y of (Y,dY) has finite Hausdor 2-measure, the boundary ∂Y=Y\Y is homeomorphic to S1, and there exists a homeo-morphism φ:D→(Y,dY) that is quasiconformal in the geometric sense. We show that φ has a continuous, monotone, and surjective extension Φ:D→Y. This result is best possible in this generality. In addition, we find a necessary and suffcient condition for Φ to be a quasiconformal homeomorphism. We provide suffcient conditions for the restriction of Φ to S1 being a quasisymmetry and to ∂Y being bi-Lipschitz equivalent to a quasicircle in the plane.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofseriesAnalysis and Geometry in Metric Spaces
dc.rightsCC BY 4.0
dc.subject.otherquasiconformal
dc.subject.othermetric surface
dc.subject.otherCarathéodory
dc.subject.otherBeurling–Ahlfors
dc.titleQuasiconformal Jordan Domains
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202111105603
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineMathematicsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange167-185
dc.relation.issn2299-3274
dc.relation.numberinseries1
dc.relation.volume9
dc.type.versionpublishedVersion
dc.rights.copyright© 2021 Toni Ikonen, published by De Gruyter.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber308659
dc.subject.ysometriset avaruudet
dc.subject.ysofunktioteoria
dc.subject.ysomittateoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27753
jyx.subject.urihttp://www.yso.fi/onto/yso/p18494
jyx.subject.urihttp://www.yso.fi/onto/yso/p13386
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1515/agms-2020-0127
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationThe author was supported by the Academy of Finland, project number 308659 and by the Vilho, Yrjö and Kalle Väisälä Foundation.
dc.type.okmA1


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