Volume 22, issue 2 (2018)

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Long-time behavior of $3$–dimensional Ricci flow, D: Proof of the main results

Richard H Bamler

Geometry & Topology 22 (2018) 949–1068

This is the fourth and last part of a series of papers on the long-time behavior of 3–dimensional Ricci flows with surgery. In this paper, we prove our main two results. The first result states that if the surgeries are performed correctly, then the flow becomes nonsingular eventually and the curvature is bounded by Ct1. The second result provides 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, collapsing theory of $3$–manifolds, topology of $3$–manifolds, geometrization conjecture
Mathematical Subject Classification 2010
Primary: 53C44
Secondary: 49Q05, 53C23, 57M15, 57M20
Received: 16 December 2014
Revised: 22 December 2016
Accepted: 21 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