#### Volume 22, issue 2 (2018)

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Long-time behavior of $3$–dimensional Ricci flow, A: Generalizations of Perelman's long-time estimates

### Richard H Bamler

Geometry & Topology 22 (2018) 775–844
##### Abstract

This is the first of a series of papers on the long-time behavior of $3$–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.

##### Keywords
Ricci flow, Ricci flow with surgery, $3$–manifolds, collapsing theory, long-time estimates for Ricci flows
##### Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 53C23, 57M50