Näytä suppeat kuvailutiedot

dc.contributor.authorLe Donne, Enrico
dc.contributor.authorZüst, Roger
dc.date.accessioned2021-09-01T07:03:24Z
dc.date.available2021-09-01T07:03:24Z
dc.date.issued2021
dc.identifier.citationLe Donne, E., & Züst, R. (2021). Space of signatures as inverse limits of Carnot groups. <i>ESAIM : Control, Optimisation and Calculus of Variations</i>, <i>27</i>, Article 37. <a href="https://doi.org/10.1051/cocv/2021040" target="_blank">https://doi.org/10.1051/cocv/2021040</a>
dc.identifier.otherCONVID_89793530
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/77624
dc.description.abstractWe formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherEDP Sciences
dc.relation.ispartofseriesESAIM : Control, Optimisation and Calculus of Variations
dc.rightsIn Copyright
dc.subject.othersignature of paths
dc.subject.otherinverse limit
dc.subject.otherpath lifting property
dc.subject.othersubmetry
dc.subject.othermetric tree
dc.subject.otherCarnot group
dc.subject.otherfree nilpotent group
dc.subject.othersub-Riemannian distance
dc.titleSpace of signatures as inverse limits of Carnot groups
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202109014749
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.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.relation.issn1292-8119
dc.relation.volume27
dc.type.versionpublishedVersion
dc.rights.copyright© EDP Sciences, SMAI 2021
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber288501
dc.relation.grantnumber713998
dc.relation.grantnumber713998
dc.relation.grantnumber322898
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/713998/EU//GeoMeG
dc.subject.ysomittateoria
dc.subject.ysodifferentiaaligeometria
dc.subject.ysostokastiset prosessit
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/p11400
jyx.subject.urihttp://www.yso.fi/onto/yso/p12497
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1051/cocv/2021040
dc.relation.funderResearch Council of Finlanden
dc.relation.funderEuropean Commissionen
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
dc.relation.funderEuroopan komissiofi
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramAcademy Research Fellow, AoFen
jyx.fundingprogramERC Starting Granten
jyx.fundingprogramAcademy Project, AoFen
jyx.fundingprogramAkatemiatutkija, SAfi
jyx.fundingprogramERC Starting Grantfi
jyx.fundingprogramAkatemiahanke, SAfi
jyx.fundinginformationE.L.D. was partially supported by the Academy of Finland (grant 288501 ‘Geometry of subRiemannian groups’ and by 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’).
dc.type.okmA1


Aineistoon kuuluvat tiedostot

Thumbnail

Aineisto kuuluu seuraaviin kokoelmiin

Näytä suppeat kuvailutiedot

In Copyright
Ellei muuten mainita, aineiston lisenssi on In Copyright