Volume 22, issue 2 (2018)

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Long-time behavior of $3$–dimensional Ricci flow: introduction

Richard H Bamler

Geometry & Topology 22 (2018) 757–774

In the following series of papers we analyze the long-time behavior of 3–dimensional Ricci flows with surgery. Our main result will be that if the surgeries are performed correctly, then only finitely many surgeries occur and after some time the curvature is bounded by Ct1. This result confirms a conjecture of Perelman. In the course of the proof, we also obtain a qualitative description of the geometry as t .

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Ricci flow, Ricci flow with surgery, finitely many surgeries, asymptotics of Ricci flow, $3$–manifolds, geometrization of $3$–manifolds
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 49Q05, 53C23, 57M15, 57M20, 57M50
Received: 16 December 2014
Revised: 1 May 2016
Accepted: 20 January 2017
Published: 16 January 2018
Proposed: Tobias H. Colding
Seconded: Bruce Kleiner, Gang Tian
Richard H Bamler
Department of Mathematics
University of California
Berkeley, CA
United States