dc.contributor.author | Julin, Vesa | |
dc.contributor.author | Niinikoski, Joonas | |
dc.date.accessioned | 2023-06-07T11:27:52Z | |
dc.date.available | 2023-06-07T11:27:52Z | |
dc.date.issued | 2023 | |
dc.identifier.citation | Julin, V., & Niinikoski, J. (2023). Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow. <i>Analysis and PDE</i>, <i>16</i>(3), 679-710. <a href="https://doi.org/10.2140/apde.2023.16.679" target="_blank">https://doi.org/10.2140/apde.2023.16.679</a> | |
dc.identifier.other | CONVID_183485861 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/87518 | |
dc.description.abstract | We prove a new quantitative version of the Alexandrov theorem which states that if the mean curvature of a regular set in Rn+1 is close to a constant in the Ln sense, then the set is close to a union of disjoint balls with respect to the Hausdorff distance. This result is more general than the previous quantifications of the Alexandrov theorem, and using it we are able to show that in R2 and R3 a weak solution of the volume preserving mean curvature flow starting from a set of finite perimeter asymptotically convergences to a disjoint union of equisize balls, up to possible translations. Here by a weak solution we mean a flat flow, obtained via the minimizing movements scheme. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | eng | |
dc.publisher | Mathematical Sciences Publishers | |
dc.relation.ispartofseries | Analysis and PDE | |
dc.rights | CC BY 4.0 | |
dc.subject.other | mean curvature flow | |
dc.subject.other | large time behavior | |
dc.subject.other | constant mean curvature | |
dc.subject.other | minimizing movements | |
dc.title | Quantitative Alexandrov theorem and asymptotic behavior of the volume preserving mean curvature flow | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202306073588 | |
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 | Analyysin ja dynamiikan tutkimuksen huippuyksikkö | fi |
dc.contributor.oppiaine | Mathematics | en |
dc.contributor.oppiaine | Analysis and Dynamics Research (Centre of Excellence) | 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 | 679-710 | |
dc.relation.issn | 2157-5045 | |
dc.relation.numberinseries | 3 | |
dc.relation.volume | 16 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © 2023 the Authors | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 314227 | |
dc.subject.yso | differentiaaligeometria | |
dc.subject.yso | osittaisdifferentiaaliyhtälöt | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p12392 | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.2140/apde.2023.16.679 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Research costs of Academy Research Fellow, AoF | en |
jyx.fundingprogram | Akatemiatutkijan tutkimuskulut, SA | fi |
jyx.fundinginformation | This research was supported by the Academy of Finland grant 314227. | |
dc.type.okm | A1 | |