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

TL;DR

This paper investigates the stability of derivations and their associated flows under weak convergence of metric measure spaces, establishing key stability results under curvature assumptions.

Contribution

It provides new stability results for derivations and flows in metric measure spaces with weakly converging measures, under curvature conditions.

Findings

Stability results for derivations under weak convergence.

Convergence of flows associated to derivations.

Results depend on curvature assumptions.

Abstract

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.