dc.contributor.author | Schultz, Timo | |
dc.date.accessioned | 2020-12-09T07:10:22Z | |
dc.date.available | 2020-12-09T07:10:22Z | |
dc.date.issued | 2021 | |
dc.identifier.citation | Schultz, T. (2021). On one-dimensionality of metric measure spaces. <i>Proceedings of the American Mathematical Society</i>, <i>149</i>(1), 383-396. <a href="https://doi.org/10.1090/proc/15162" target="_blank">https://doi.org/10.1090/proc/15162</a> | |
dc.identifier.other | CONVID_47292076 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/73037 | |
dc.description.abstract | In this paper, we prove that a metric measure space which has at least one open set isometric to an interval, and for which the (possibly non-unique) optimal transport map exists from any absolutely continuous measure to an arbitrary measure, is a one-dimensional manifold (possibly with boundary). As an immediate corollary we obtain that if a metric measure space is a very strict CD(K, N) -space or an essentially non-branching MCP(K, N)-space with some open set isometric to an interval, then it is a one-dimensional manifold. We also obtain the same conclusion for a metric measure space which has a point in which the Gromov-Hausdorff tangent is unique and isometric to the real line, and for which the optimal transport maps not only exist but are unique. Again, we obtain an analogous corollary in the setting of essentially non-branching MCP(K, N)-spaces | en |
dc.format.mimetype | application/pdf | |
dc.language | eng | |
dc.language.iso | eng | |
dc.publisher | American Mathematical Society (AMS) | |
dc.relation.ispartofseries | Proceedings of the American Mathematical Society | |
dc.rights | CC BY-NC-ND 4.0 | |
dc.subject.other | optimal transport | |
dc.subject.other | Ricci curvature | |
dc.subject.other | metric measure spaces | |
dc.subject.other | Gromov--Hausdorff tangents | |
dc.title | On one-dimensionality of metric measure spaces | |
dc.type | research article | |
dc.identifier.urn | URN:NBN:fi:jyu-202012096980 | |
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 | 383-396 | |
dc.relation.issn | 0002-9939 | |
dc.relation.numberinseries | 1 | |
dc.relation.volume | 149 | |
dc.type.version | acceptedVersion | |
dc.rights.copyright | © 2020 American Mathematical Society | |
dc.rights.accesslevel | openAccess | fi |
dc.type.publication | article | |
dc.relation.grantnumber | 314789 | |
dc.subject.yso | differentiaaligeometria | |
dc.subject.yso | metriset avaruudet | |
dc.subject.yso | mittateoria | |
dc.format.content | fulltext | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p16682 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p27753 | |
jyx.subject.uri | http://www.yso.fi/onto/yso/p13386 | |
dc.rights.url | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.relation.doi | 10.1090/proc/15162 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundinginformation | The author acknowledges the support by the Academy of Finland, project #314789 | |
dc.type.okm | A1 | |