{"title":"On gluing Alexandrov spaces with lower Ricci curvature bounds","authors":"Kapovitch,Vitali, Ketterer,Christian, Sturm,Karl-Theodor","doi":"10.4310/cag.2023.v31.n6.a6","DOIUrl":null,"url":null,"abstract":"In this paper we prove that in the class of metric measure space with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition $RCD^*(K,N)$ with $K\\in \\mathbb{R}$ & $N\\in [1,\\infty)$ is preserved under doubling and gluing constructions provided the weight in the measure is semiconcave.","PeriodicalId":50662,"journal":{"name":"Communications in Analysis and Geometry","volume":"56 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/cag.2023.v31.n6.a6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
In this paper we prove that in the class of metric measure space with Alexandrov curvature bounded from below the Riemannian curvature-dimension condition $RCD^*(K,N)$ with $K\in \mathbb{R}$ & $N\in [1,\infty)$ is preserved under doubling and gluing constructions provided the weight in the measure is semiconcave.
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