dc.contributor.author | Ikonen, Toni | |
dc.date.accessioned | 2021-11-10T11:17:29Z | |
dc.date.available | 2021-11-10T11:17:29Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Ikonen, 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.other | CONVID_101837523 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/78585 | |
dc.description.abstract | We 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.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Walter de Gruyter GmbH | |
dc.relation.ispartofseries | Analysis and Geometry in Metric Spaces | |
dc.rights | CC BY 4.0 | |
dc.subject.other | quasiconformal | |
dc.subject.other | metric surface | |
dc.subject.other | Carathéodory | |
dc.subject.other | Beurling–Ahlfors | |
dc.title | Quasiconformal Jordan Domains | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202111105603 | |
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.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 167-185 | |
dc.relation.issn | 2299-3274 | |
dc.relation.numberinseries | 1 | |
dc.relation.volume | 9 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2021 Toni Ikonen, published by De Gruyter. | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 308659 | |
dc.subject.yso | metriset avaruudet | |
dc.subject.yso | funktioteoria | |
dc.subject.yso | mittateoria | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27753 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p18494 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p13386 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1515/agms-2020-0127 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundinginformation | The author was supported by the Academy of Finland, project number 308659 and by the Vilho, Yrjö and Kalle Väisälä Foundation. | |
dc.type.okm | A1 | |