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2008 Width and finite extinction time of Ricci flow
Tobias H Colding, William P Minicozzi II
Geom. Topol. 12(5): 2537-2586 (2008). DOI: 10.2140/gt.2008.12.2537


This is an expository article with complete proofs intended for a general nonspecialist audience. The results are two-fold. First, we discuss a geometric invariant, that we call the width, of a manifold and show how it can be realized as the sum of areas of minimal 2–spheres. For instance, when M is a homotopy 3–sphere, the width is loosely speaking the area of the smallest 2–sphere needed to ‘pull over’ M. Second, we use this to conclude that Hamilton’s Ricci flow becomes extinct in finite time on any homotopy 3–sphere.


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Tobias H Colding. William P Minicozzi II. "Width and finite extinction time of Ricci flow." Geom. Topol. 12 (5) 2537 - 2586, 2008.


Received: 30 June 2007; Accepted: 10 October 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1161.53352
MathSciNet: MR2460871
Digital Object Identifier: 10.2140/gt.2008.12.2537

Primary: 53C42 , 53C44
Secondary: 58E12 , 58E20

Keywords: bubble convergence , extinction , Harmonic map , min-max , Ricci flow , sweepout , width

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.12 • No. 5 • 2008
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