dc.contributor.author | Eriksson-Bique, Sylvester | |
dc.contributor.author | Gartland, Chris | |
dc.contributor.author | Le Donne, Enrico | |
dc.contributor.author | Naples, Lisa | |
dc.contributor.author | Nicolussi Golo, Sebastiano | |
dc.date.accessioned | 2022-10-26T09:53:57Z | |
dc.date.available | 2022-10-26T09:53:57Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Eriksson-Bique, S., Gartland, C., Le Donne, E., Naples, L., & Nicolussi Golo, S. (2023). Nilpotent Groups and Bi-Lipschitz Embeddings Into L1. <i>International Mathematics Research Notices</i>, <i>2023</i>(12), 10759-10797. <a href="https://doi.org/10.1093/imrn/rnac264" target="_blank">https://doi.org/10.1093/imrn/rnac264</a> | |
dc.identifier.other | CONVID_159301233 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/83706 | |
dc.description.abstract | We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an L1 space, then it is abelian. We reach this conclusion by proving that every Carnot group that bi-Lipschitz embeds into L1 is abelian. Our proof follows the work of Cheeger and Kleiner, by considering the pull-back distance of a Lipschitz map into L1 and representing it using a cut measure. We show that such cut measures, and the induced distances, can be blown up and the blown-up cut measure is supported on “generic” tangents of the original sets. By repeating such a blow-up procedure, one obtains a cut measure supported on half-spaces. This differentiation result then is used to prove that bi-Lipschitz embeddings can not exist in the non-abelian settings. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Oxford University Press (OUP) | |
dc.relation.ispartofseries | International Mathematics Research Notices | |
dc.rights | CC BY 4.0 | |
dc.title | Nilpotent Groups and Bi-Lipschitz Embeddings Into L1 | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202210265015 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Analyysin ja dynamiikan tutkimuksen huippuyksikkö | fi |
dc.contributor.oppiaine | Geometrinen analyysi ja matemaattinen fysiikka | fi |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Analysis and Dynamics Research (Centre of Excellence) | en |
dc.contributor.oppiaine | Geometric Analysis and Mathematical Physics | en |
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 | 10759-10797 | |
dc.relation.issn | 1073-7928 | |
dc.relation.numberinseries | 12 | |
dc.relation.volume | 2023 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © The Author(s) 2022. Published by Oxford University Press. | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 328846 | |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 713998 | |
dc.relation.grantnumber | 322898 | |
dc.relation.grantnumber | 288501 | |
dc.relation.projectid | info:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG | |
dc.subject.yso | differentiaaligeometria | |
dc.subject.yso | funktionaalianalyysi | |
dc.subject.yso | metriset avaruudet | |
dc.subject.yso | ryhmäteoria | |
dc.subject.yso | Lien ryhmät | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p17780 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27753 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p12497 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p39641 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1093/imrn/rnac264 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | European Commission | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Euroopan komissio | fi |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Research costs of Academy Research Fellow, AoF | en |
jyx.fundingprogram | ERC Starting Grant | en |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Academy Research Fellow, AoF | en |
jyx.fundingprogram | Akatemiatutkijan tutkimuskulut, SA | fi |
jyx.fundingprogram | ERC Starting Grant | fi |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundingprogram | Akatemiatutkija, SA | fi |
jyx.fundinginformation | S.E.-B. was supported partially by the Finnish Academy [grant # 345005]. E.L.D. was partially supported by the Academy of Finland [grant 288501 “Geometry of Sub-Riemannian Groups” and grant 322898 “Sub-Riemannian Geometry via Metric-Geometry and Lie-Group Theory”] and by the European Research Council [ERC Starting Grant 713998 GeoMeG “Geometry of Metric Groups”]. S.N.G. was supported by the Academy of Finland [grant 328846 “Singular Integrals, Harmonic Functions, and Boundary Regularity in Heisenberg Groups”, grant 322898 “Sub-Riemannian Geometry via Metric-Geometry and Lie-Group Theory”, and grant 314172 “Quantitative Rectifiability in Euclidean and Non-Euclidean Spaces”]. | |
dc.type.okm | A1 | |