This is the first of a series of papers on the long-time behavior of –dimensional Ricci flows with surgery. We first fix a notion of Ricci flows with surgery, which will be used in this and the following three papers. Then we review Perelman’s long-time estimates and generalize them to the case in which the underlying manifold is allowed to have a boundary. Eventually, making use of Perelman’s techniques, we prove new long-time estimates, which hold whenever the metric is sufficiently collapsed.
"Long-time behavior of $3$–dimensional Ricci flow, A: Generalizations of Perelman's long-time estimates." Geom. Topol. 22 (2) 775 - 844, 2018. https://doi.org/10.2140/gt.2018.22.775