dc.contributor.author | Rajala, Kai | |
dc.date.accessioned | 2017-02-14T11:31:32Z | |
dc.date.available | 2017-08-25T21:45:08Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Rajala, K. (2017). Uniformization of two-dimensional metric surfaces. <i>Inventiones mathematicae</i>, <i>207</i>(3), 1301-1375. <a href="https://doi.org/10.1007/s00222-016-0686-0" target="_blank">https://doi.org/10.1007/s00222-016-0686-0</a> | |
dc.identifier.other | CONVID_26186503 | |
dc.identifier.other | TUTKAID_71028 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/53029 | |
dc.description.abstract | We establish uniformization results for metric spaces that
are homeomorphic to the Euclidean plane or sphere and have locally
finite Hausdorff 2-measure. Applying the geometric definition of quasiconformality,
we give a necessary and sufficient condition for such spaces
to be QC equivalent to the Euclidean plane, disk, or sphere. Moreover,
we show that if such a QC parametrization exists, then the dilatation
can be bounded by 2. As an application, we show that the Euclidean
upper bound for measures of balls is a sufficient condition for the existence
of a 2-QC parametrization. This result gives a new approach
to the Bonk-Kleiner theorem on parametrizations of Ahlfors 2-regular
spheres by quasisymmetric maps. | |
dc.language.iso | eng | |
dc.publisher | Springer | |
dc.relation.ispartofseries | Inventiones mathematicae | |
dc.subject.other | metric surfaces | |
dc.title | Uniformization of two-dimensional metric surfaces | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201702141437 | |
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 | 2017-02-14T10:15:15Z | |
dc.type.coar | journal article | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 1301-1375 | |
dc.relation.issn | 0020-9910 | |
dc.relation.numberinseries | 3 | |
dc.relation.volume | 207 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © Springer-Verlag Berlin Heidelberg 2016. This is a final draft version of an article whose final and definitive form has been published by Springer. Published in this repository with the kind permission of the publisher. | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.doi | 10.1007/s00222-016-0686-0 | |