{"title":"Multi-marginal optimal transport on the Heisenberg group","authors":"Brendan Pass, A. Pinamonti, Mattia Vedovato","doi":"10.4310/maa.2021.v28.n1.a5","DOIUrl":null,"url":null,"abstract":"We consider the multi-marginal optimal transport of aligning several compactly supported marginals on the Heisenberg group to minimize the total cost, which we take to be the sum of the squared Carnot-Caratheodory distances from the marginal points to their barycenter. Under certain technical hypotheses, we prove existence and uniqueness of optimal maps. We also point out several related open questions.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Methods and applications of analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4310/maa.2021.v28.n1.a5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 2
Abstract
We consider the multi-marginal optimal transport of aligning several compactly supported marginals on the Heisenberg group to minimize the total cost, which we take to be the sum of the squared Carnot-Caratheodory distances from the marginal points to their barycenter. Under certain technical hypotheses, we prove existence and uniqueness of optimal maps. We also point out several related open questions.
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