Stability of RCD condition under concentration topology

Ryunosuke Ozawa, Takumi Yokota

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2019 Aug 1


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