Stability of RCD condition under concentration topology

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Abstract

We prove the stability of the Riemannian curvature dimension condition introduced by Ambrosio–Gigli–Savaré under the concentration of metric measure spaces introduced by Gromov. This is an analogue of the result of Funano–Shioya for the curvature dimension condition of Lott–Villani and Sturm. These conditions are synthetic lower Ricci curvature bound for metric measure spaces. En route, we also prove the convergence of the Cheeger energy in our setting.

Original languageEnglish
Article number151
JournalCalculus of Variations and Partial Differential Equations
Volume58
Issue number4
DOIs
Publication statusPublished - 2019 Aug 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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