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dc.contributor.authorIkonen, Toni
dc.contributor.authorPasqualetto, Enrico
dc.contributor.authorSoultanis, Elefterios
dc.date.accessioned2021-11-11T10:26:33Z
dc.date.available2021-11-11T10:26:33Z
dc.date.issued2022
dc.identifier.citationIkonen, T., Pasqualetto, E., & Soultanis, E. (2022). Abstract and concrete tangent modules on Lipschitz differentiability spaces. <i>Proceedings of the American Mathematical Society</i>, <i>150</i>, 327-343. <a href="https://doi.org/10.1090/proc/15656" target="_blank">https://doi.org/10.1090/proc/15656</a>
dc.identifier.otherCONVID_101849807
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/78616
dc.description.abstractWe construct an isometric embedding from Gigli’s abstract tangent module into the concrete tangent module of a space admitting a (weak) Lipschitz differentiable structure, and give two equivalent conditions which characterize when the embedding is an isomorphism. Together with arguments from Bate, Kangasniemi, and Orponen, Cheeger’s differentiation theorem via the multilinear Kakeya inequality, arXiv:1904.00808 (2019), this equivalence is used to show that the –-type condition self-improves to . We also provide a direct proof of a result by Gigli and Pasqualetto, Equivalence of two different notions of tangent bundle on rectifiable metric measure spaces, arXiv:1611.09645 that, for a space with a strongly rectifiable decomposition, Gigli’s tangent module admits an isometric embedding into the so-called Gromov–Hausdorff tangent module, without any a priori reflexivity assumptions.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherAmerican Mathematical Society (AMS)
dc.relation.ispartofseriesProceedings of the American Mathematical Society
dc.rightsCC BY-NC-ND 4.0
dc.titleAbstract and concrete tangent modules on Lipschitz differentiability spaces
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202111115634
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.description.reviewstatuspeerReviewed
dc.format.pagerange327-343
dc.relation.issn0002-9939
dc.relation.volume150
dc.type.versionacceptedVersion
dc.rights.copyright© 2021 American Mathematical Society
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber
dc.relation.grantnumber
dc.relation.grantnumber308659
dc.relation.grantnumber314789
dc.subject.ysometriset avaruudet
dc.subject.ysoekvivalenssi
dc.subject.ysomatematiikka
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27753
jyx.subject.urihttp://www.yso.fi/onto/yso/p16524
jyx.subject.urihttp://www.yso.fi/onto/yso/p3160
dc.rights.urlhttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi10.1090/proc/15656
dc.relation.funderVilho, Yrjö ja Kalle Väisälän rahastofi
dc.relation.funderVilho, Yrjö ja Kalle Väisälän rahastofi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderSuomen Akatemiafi
dc.relation.funderVäisälä Foundationen
dc.relation.funderVäisälä Foundationen
dc.relation.funderAcademy of Finlanden
dc.relation.funderAcademy of Finlanden
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAcademy Project, AoFen
jyx.fundinginformationThe first author was supported by the Academy of Finland, project number 308659, and by the Vilho, Yrjö and Kalle Väisälä Foundation. The second author was supported by the Academy of Finland, project number 314789, and by the Balzan project led by Prof. Luigi Ambrosio. The third author was supported by the Swiss National Foundation, grant no. 182423.


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