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dc.contributor.authorLe Donne, Enrico
dc.contributor.authorMoisala, Terhi
dc.date.accessioned2021-05-19T11:26:01Z
dc.date.available2021-05-19T11:26:01Z
dc.date.issued2021
dc.identifier.citationLe Donne, E., & Moisala, T. (2021). Semigenerated Carnot algebras and applications to sub-Riemannian perimeter. <i>Mathematische Zeitschrift</i>, <i>299</i>(3-4), 2257-2285. <a href="https://doi.org/10.1007/s00209-021-02744-4" target="_blank">https://doi.org/10.1007/s00209-021-02744-4</a>
dc.identifier.otherCONVID_83393804
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/75757
dc.description.abstractThis paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our viewpoint is algebraic: such a phenomenon happens if and only if the semigroup generated by each horizontal half-space is a vertical half-space. We call semigenerated those Carnot groups with this property. For Carnot groups of nilpotency step 3 we provide a complete characterization of semigeneration in terms of whether such groups do not have any Engel-type quotients. Engel-type groups, which are introduced here, are the minimal (in terms of quotients) counterexamples. In addition, we give some sufficient criteria for semigeneration of Carnot groups of arbitrary step. For doing this, we define a new class of Carnot groups, which we call type (◊)(◊) and which generalizes the previous notion of type (⋆)(⋆) defined by M. Marchi. As an application, we get that in type (◊)(◊) groups and in step 3 groups that do not have any Engel-type algebra as a quotient, one achieves a strong rectifiability result for sets of finite perimeter in the sense of Franchi, Serapioni, and Serra-Cassano.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherSpringer
dc.relation.ispartofseriesMathematische Zeitschrift
dc.rightsCC BY 4.0
dc.subject.otherCarnot algebra
dc.subject.otherhorizontal half-space
dc.subject.othersemigroup generated
dc.subject.otherLie wedge
dc.subject.otherconstant intrinsic normal
dc.subject.otherfinite sub-Riemannian perimeter
dc.subject.otherEngel-type algebras
dc.subject.othertipe diamond
dc.subject.othertrimmed algebra
dc.titleSemigenerated Carnot algebras and applications to sub-Riemannian perimeter
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202105193022
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineGeometrinen analyysi ja matemaattinen fysiikkafi
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineAnalyysin ja dynamiikan tutkimuksen huippuyksikköfi
dc.contributor.oppiaineGeometric Analysis and Mathematical Physicsen
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineAnalysis and Dynamics Research (Centre of Excellence)en
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.description.reviewstatuspeerReviewed
dc.format.pagerange2257-2285
dc.relation.issn0025-5874
dc.relation.numberinseries3-4
dc.relation.volume299
dc.type.versionpublishedVersion
dc.rights.copyright© The Author(s) 2021
dc.rights.accesslevelopenAccessfi
dc.subject.ysomittateoria
dc.subject.ysodifferentiaaligeometria
dc.subject.ysoryhmäteoria
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p13386
jyx.subject.urihttp://www.yso.fi/onto/yso/p16682
jyx.subject.urihttp://www.yso.fi/onto/yso/p12497
dc.rights.urlhttps://creativecommons.org/licenses/by/4.0/
dc.relation.doi10.1007/s00209-021-02744-4
jyx.fundinginformationOpen access funding provided by University of Jyväskylä (JYU).


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