Stability of RCD condition under concentration topology
Stability of RCD condition under concentration topology
复制标题
浓度拓扑下 RCD 条件的稳定性
DOI：
10.1007/s00526-019-1586-0
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Ryunosuke Ozawa and Takumi Yokota
中科院分区：
文献类型：
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作者：
Shin-ichi Ohta;Asuka Takatsu;Ryunosuke Ozawa and Takumi Yokota
证明了Ambrosio-Gigli-Savaré引入的黎曼曲率维数条件在Gromov引入的度量测度空间集中下的稳定性.这是Funano-Shioya关于Lott-Villani和Sturm的曲率维数条件的结果的类似。这些条件是度量测度空间的合成Ricci曲率下界。在途中，我们还证明了收敛的Cheeger能源在我们的设置。
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.