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dc.contributor.authorLe Donne, Enrico
dc.contributor.authorNicolussi Golo, Sebastiano
dc.date.accessioned2018-12-21T10:41:49Z
dc.date.available2018-12-21T10:41:49Z
dc.date.issued2018
dc.identifier.citationLe Donne, E., & Nicolussi Golo, S. (2018). Regularity properties of spheres in homogeneous groups. <i>Transactions of the American Mathematical Society</i>, <i>370</i>, 2057-2084. <a href="https://doi.org/10.1090/tran/7038" target="_blank">https://doi.org/10.1090/tran/7038</a>
dc.identifier.otherCONVID_27337283
dc.identifier.otherTUTKAID_75614
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/60810
dc.description.abstractWe study left-invariant distances on Lie groups for which there exists a one-parameter family of homothetic automorphisms. The main examples are Carnot groups, in particular the Heisenberg group with the standard dilations. We are interested in criteria implying that, locally and away from the diagonal, the distance is Euclidean Lipschitz and, consequently, that the metric spheres are boundaries of Lipschitz domains in the Euclidean sense. In the first part of the paper, we consider geodesic distances. In this case, we actually prove the regularity of the distance in the more general context of sub-Finsler manifolds with no abnormal geodesics. Secondly, for general groups we identify an algebraic criterium in terms of the dilating automorphisms, which for example makes us conclude the regularity of every homogeneous distance on the Heisenberg group. In such a group, we analyze in more detail the geometry of metric spheres. We also provide examples of homogeneous groups where spheres present cusps.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society
dc.relation.ispartofseriesTransactions of the American Mathematical Society
dc.rightsCC-BY-NC-ND 4.0
dc.subject.otherregularity properties
dc.subject.otherspheres
dc.subject.otherhomogeneous groups
dc.titleRegularity properties of spheres in homogeneous groups
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-201812215309
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.updated2018-12-21T07:15:27Z
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2057-2084
dc.relation.issn0002-9947
dc.relation.numberinseries0
dc.relation.volume370
dc.type.versionacceptedVersion
dc.rights.copyright© 2017 American Mathematical Society.
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber288501
dc.relation.grantnumber607643
dc.relation.grantnumber607643
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/607643/EU//
dc.subject.ysojoukot (matematiikka)
dc.subject.ysoalgebra
dc.subject.ysomatematiikka
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p12530
jyx.subject.urihttp://www.yso.fi/onto/yso/p12498
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1090/tran/7038
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderAcademy of Finlanden
dc.relation.funderEuropean Commissionen
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramEU:n 7. puiteohjelma (FP7)fi
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramFP7 (EU's 7th Framework Programme)en
jyx.fundinginformationThe first author was supported by the Academy of Finland project No. 288501. The second author was supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement No. 607643.
dc.type.okmA1


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