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

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, m(n)), m(n) weakly convergent to m. In particular, under curvature assumptions, either only on the limit metric structure (X, d, m) or on the whole sequence of metric measure spaces, we provide several stability results. (C) 2016 Elsevier Inc. All rights reserved.