Abstract
The metric flow is introduced and extensively studied by Bamler [Compactness theory of the space of super Ricci flows, preprint (2020), arXiv:2008.09298; Structure theory of non-collapsed limits of Ricci flows, preprint (2020), arXiv:2009.03243], especially as an [Formula: see text]-limit of a sequence of smooth Ricci flows with uniformly bounded Nash entropy, in which case each regular point on the limit is a point of smooth convergence. In this note, we shall consider the [Formula: see text]-convergence of a sequence of [Formula: see text]-limit flows, and, like Bamler, show that each regular point on the limit is also a point of smooth convergence. The main result will be applied in another work of the authors [P.-Y. Chan, Z. Ma and Y. Zhang, Dimension reduction for positively curved steady solitons, preprint (2023), arXiv:2310.14020].
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