A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries

Le Donne, Enrico

doi:10.1515/agms-2017-0007

dc.contributor.author	Le Donne, Enrico
dc.date.accessioned	2018-01-31T08:00:39Z
dc.date.available	2018-01-31T08:00:39Z
dc.date.issued	2017
dc.identifier.citation	Le Donne, E. (2017). A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries. <i>Analysis and Geometry in Metric Spaces</i>, <i>5</i>(1), 116-137. <a href="https://doi.org/10.1515/agms-2017-0007" target="_blank">https://doi.org/10.1515/agms-2017-0007</a>
dc.identifier.other	CONVID_27879044
dc.identifier.other	TUTKAID_76687
dc.identifier.uri	https://jyx.jyu.fi/handle/123456789/56960
dc.description.abstract	Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory spaces and of nilpotent metric Lie groups.
dc.language.iso	eng
dc.publisher	De Gruyter Open
dc.relation.ispartofseries	Analysis and Geometry in Metric Spaces
dc.subject.other	Carnot groups
dc.subject.other	sub-Riemannian geometry
dc.subject.other	sub-Finsler geometry
dc.subject.other	homogeneous spaces
dc.subject.other	homogeneous groups
dc.subject.other	nilpotent groups
dc.subject.other	metric groups
dc.title	A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries
dc.type	article
dc.identifier.urn	URN:NBN:fi:jyu-201801301378
dc.contributor.laitos	Matematiikan ja tilastotieteen laitos	fi
dc.contributor.laitos	Department of Mathematics and Statistics	en
dc.contributor.oppiaine	Matematiikka	fi
dc.contributor.oppiaine	Mathematics	en
dc.type.uri	http://purl.org/eprint/type/JournalArticle
dc.date.updated	2018-01-30T13:15:13Z
dc.type.coar	http://purl.org/coar/resource_type/c_dcae04bc
dc.description.reviewstatus	peerReviewed
dc.format.pagerange	116-137
dc.relation.issn	2299-3274
dc.relation.numberinseries	1
dc.relation.volume	5
dc.type.version	publishedVersion
dc.rights.copyright	© 2017 Enrico Le Donne, published by De Gruyter Open. This is an open access article distributed under the terms of the Creative Commons License.
dc.rights.accesslevel	openAccess	fi
dc.subject.yso	differentiaaligeometria
dc.subject.yso	ryhmäteoria
jyx.subject.uri	http://www.yso.fi/onto/yso/p16682
jyx.subject.uri	http://www.yso.fi/onto/yso/p12497
dc.rights.url	https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.relation.doi	10.1515/agms-2017-0007
dc.type.okm	A2