Weak and strong convergence of derivations and stability of flows with respect to MGH convergence

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• 作者：Luigi Ambrosio^a ; ^{luigi.ambrosio@sns.it} ; Federico Stra^a ; ^{federico.stra@sns.it} ; Dario Trevisan^b ; ^{dario.trevisan@unipi.it}
• 关键词：Derivations ; Measured Gromov&ndash ; Hausdorff convergence ; Cheeger energy
• 刊名：Journal of Functional Analysis
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：272
• 期：3
• 页码：1182-1229
• 全文大小：758 K
• 卷排序：272

文摘

This paper is devoted to the study of weak and strong convergence of derivations, and of the flows associated to them, when dealing with a sequence of metric measure structures (X,d,mn)(X,d,mn), mnmn weakly convergent to mm. In particular, under curvature assumptions, either only on the limit metric structure (X,d,m)(X,d,m) or on the whole sequence of metric measure spaces, we provide several stability results.