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dc.contributor.authorRomney, Matthew
dc.date.accessioned2019-06-10T09:43:28Z
dc.date.available2021-08-01T21:35:09Z
dc.date.issued2019
dc.identifier.citationRomney, M. (2019). Singular quasisymmetric mappings in dimensions two and greater. <i>Advances in Mathematics</i>, <i>31</i>, 479-494. <a href="https://doi.org/10.1016/j.aim.2019.05.022" target="_blank">https://doi.org/10.1016/j.aim.2019.05.022</a>
dc.identifier.otherCONVID_30878693
dc.identifier.otherTUTKAID_81562
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/64478
dc.description.abstractFor all n ≥2, we construct a metric space (X, d)and a quasisymmetric mapping f:[0, 1]n→X with the property that f−1 is not absolutely continuous with respect to the Hausdorff n-measure on X. That is, there exists a Borel set E⊂[0, 1]n with Lebesgue measure |E| >0 such that f(E) has Hausdorff n-measure zero. The construction may be carried out so that X has finite Hausdorff n-measure and |E| is arbitrarily close to 1, or so that |E| =1. This gives a negative answer to a question of Heinonen and Semmes.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAcademic Press
dc.relation.ispartofseriesAdvances in Mathematics
dc.rightsCC BY-NC-ND 4.0
dc.subject.otherquasiconformal mapping
dc.subject.othermetric space
dc.subject.otherabsolute continuity
dc.titleSingular quasisymmetric mappings in dimensions two and greater
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201906052970
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.date.updated2019-06-05T09:15:13Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange479-494
dc.relation.issn0001-8708
dc.relation.numberinseries0
dc.relation.volume31
dc.type.versionacceptedVersion
dc.rights.copyright© 2019 Elsevier Inc.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber288501
dc.relation.grantnumber713998
dc.relation.grantnumber713998
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.ysometriset avaruudet
dc.subject.ysofunktioteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27753
jyx.subject.urihttp://www.yso.fi/onto/yso/p18494
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1016/j.aim.2019.05.022
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderAcademy of Finlanden
dc.relation.funderEuropean Commissionen
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramERC Starting Grantfi
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramERC Starting Granten
jyx.fundinginformationThis research was supported by the Academy of Finland grant 288501 and by the ERC Starting Grant 713998 GeoMeG.


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