Singular quasisymmetric mappings in dimensions two and greater

Romney, Matthew

doi:10.1016/j.aim.2019.05.022

dc.contributor.author	Romney, Matthew
dc.date.accessioned	2019-06-10T09:43:28Z
dc.date.available	2021-08-01T21:35:09Z
dc.date.issued	2019
dc.identifier.citation	Romney, 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.other	CONVID_30878693
dc.identifier.other	TUTKAID_81562
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/64478
dc.description.abstract	For 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.mimetype	application/pdf
dc.language.iso	eng
dc.publisher	Academic Press
dc.relation.ispartofseries	Advances in Mathematics
dc.rights	CC BY-NC-ND 4.0
dc.subject.other	quasiconformal mapping
dc.subject.other	metric space
dc.subject.other	absolute continuity
dc.title	Singular quasisymmetric mappings in dimensions two and greater
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201906052970
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	2019-06-05T09:15:13Z
dc.type.coar	http://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	479-494
dc.relation.issn	0001-8708
dc.relation.numberinseries	0
dc.relation.volume	31
dc.type.version	acceptedVersion
dc.rights.copyright	© 2019 Elsevier Inc.
dc.rights.accesslevel	openAccess	fi
dc.relation.grantnumber	288501
dc.relation.grantnumber	713998
dc.relation.grantnumber	713998
dc.relation.projectid	info:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.yso	metriset avaruudet
dc.subject.yso	funktioteoria
dc.format.content	fulltext
jyx.subject.uri	http://www.yso.fi/onto/yso/p27753
jyx.subject.uri	http://www.yso.fi/onto/yso/p18494
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1016/j.aim.2019.05.022
dc.relation.funder	Suomen Akatemia	fi
dc.relation.funder	Euroopan komissio	fi
dc.relation.funder	Academy of Finland	en
dc.relation.funder	European Commission	en
jyx.fundingprogram	Akatemiatutkija, SA	fi
jyx.fundingprogram	ERC Starting Grant	fi
jyx.fundingprogram	Academy Research Fellow, AoF	en
jyx.fundingprogram	ERC Starting Grant	en
jyx.fundinginformation	This research was supported by the Academy of Finland grant 288501 and by the ERC Starting Grant 713998 GeoMeG.
dc.type.okm	A1