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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Estimates for the extinction time for the Ricci flow on certain $3$-manifolds and a question of Perelman


Authors: Tobias H. Colding and William P. Minicozzi II
Journal: J. Amer. Math. Soc. 18 (2005), 561-569
MSC (2000): Primary 53C44; Secondary 53C42, 57M50
Published electronically: April 13, 2005
MathSciNet review: 2138137
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Abstract: We show that the Ricci flow becomes extinct in finite time on any Riemannian $3$-manifold without aspherical summands.


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Additional Information

Tobias H. Colding
Affiliation: Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
Email: colding@cims.nyu.edu

William P. Minicozzi II
Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218
Email: minicozz@math.jhu.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-05-00486-8
PII: S 0894-0347(05)00486-8
Keywords: Ricci flow, finite extinction, $3$-manifolds, min--max surfaces
Received by editor(s): October 6, 2003
Published electronically: April 13, 2005
Additional Notes: The authors were partially supported by NSF Grants DMS 0104453 and DMS 0104187
Article copyright: © Copyright 2005 American Mathematical Society