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

Bamler, Richard

doi:10.2140/gt.2018.22.757

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

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

Richard H Bamler

Geometry & Topology 22 (2018) 757–774

DOI: 10.2140/gt.2018.22.757

Abstract

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 $C t^{- 1}$ . This result confirms a conjecture of Perelman. In the course of the proof, we also obtain a qualitative description of the geometry as $t \to \infty$ .

Keywords

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

References

Publication

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

Authors

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

Volume 22, issue 2 (2018)