dc.contributor.author | Chousionis, Vasileios | |
dc.contributor.author | Fässler, Katrin | |
dc.contributor.author | Orponen, Tuomas | |
dc.date.accessioned | 2019-08-26T06:42:14Z | |
dc.date.available | 2019-08-26T06:42:14Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Chousionis, V., Fässler, K., & Orponen, T. (2019). Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group. <i>American Journal of Mathematics</i>, <i>141</i>(4), 1087-1147. <a href="https://doi.org/10.1353/ajm.2019.0028" target="_blank">https://doi.org/10.1353/ajm.2019.0028</a> | |
dc.identifier.other | CONVID_32434929 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/65300 | |
dc.description.abstract | The purpose of this paper is to introduce and study some basic concepts of quantitative rectifiability in the first Heisenberg group H. In particular, we aim to demonstrate that new phenomena arise compared to the Euclidean theory, founded by G. David and S. Semmes in the 1990s. The theory in H has an apparent connection to certain nonlinear PDEs, which do not play a role with similar questions in R3. Our main object of study are the intrinsic Lipschitz graphs in H, introduced by B. Franchi, R. Serapioni, and F. Serra Cassano in 2006. We claim that these 3-dimensional sets in H, if any, deserve to be called quantitatively 3-rectifiable. Our main result is that the intrinsic Lipschitz graphs satisfy a weak geometric lemma with respect to vertical β-numbers. Conversely, extending a result of David and Semmes from Rn, we prove that a 3-Ahlfors-David regular subset in H, which satisfies the weak geometric lemma and has big vertical projections, necessarily has big pieces of intrinsic Lipschitz graphs. | en |
dc.format.mimetype | application/pdf | |
dc.language | eng | |
dc.language.iso | eng | |
dc.publisher | Johns Hopkins University Press | |
dc.relation.ispartofseries | American Journal of Mathematics | |
dc.rights | In Copyright | |
dc.title | Intrinsic Lipschitz graphs and vertical β-numbers in the Heisenberg group | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-201908263900 | |
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.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.format.pagerange | 1087-1147 | |
dc.relation.issn | 0002-9327 | |
dc.relation.numberinseries | 4 | |
dc.relation.volume | 141 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2019 by Johns Hopkins University Press | |
dc.rights.accesslevel | openAccess | fi |
dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
dc.subject.yso | mittateoria | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p12392 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p13386 | |
dc.rights.url | http://rightsstatements.org/page/InC/1.0/?language=en | |
dc.relation.doi | 10.1353/ajm.2019.0028 | |
jyx.fundinginformation | Research of the first author supported by the Simons Foundation via the Collaboration grant Analysis and dynamics in Carnot groups, grant no. 521845; research of the second author supported by the Academy of Finland through the grant Sub-Riemannian manifolds from a quasiconformal viewpoint, grant no. 285159; research of the third author supported by the Academy of Finland through the grant Restricted families of projections, and applications to Kakeya type problems, grant no. 274512; the third author is also a member of the Finnish CoE in Analysis and Dynamics Research. | |
dc.type.okm | A1 | |