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

Bamler, Richard

doi:10.2140/gt.2018.22.775

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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

DOI: 10.2140/gt.2018.22.775

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

References

Publication

Received: 16 December 2014

Revised: 21 June 2015

Accepted: 20 January 2017

Published: 16 January 2018

Proposed: Tobias H. Colding

Seconded: Bruce Kleiner, Gang Tian

Authors

Richard H Bamler
Department of Mathematics University of California Berkeley, CA United States
https://math.berkeley.edu/~rbamler/

Volume 22, issue 2 (2018)