We study the asymptotic behavior of metric measure spaces satisfying the rough curvature dimension condition. We prove stabilities of the rough curvature dimension condition with respect to the observable distance function and the $L^2$-transportation distance function.
The first author is partly supported by the Grant-in-Aid for JSPS Fellows (No.17J02121). The second author was partly supported by JSPS KAKENHI (No.24224002), Max-Planck Institute for Mathematics, and the Grant-in-Aid for JSPS Fellows (No.17J03507).
Daisuke KAZUKAWA. Ryunosuke OZAWA. Norihiko SUZUKI. "Stabilities of rough curvature dimension condition." J. Math. Soc. Japan 72 (2) 541 - 567, April, 2020. https://doi.org/10.2969/jmsj/81468146