Estimates for the extinction time for the Ricci flow on certain -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

DOI:
https://doi.org/10.1090/S0894-0347-05-00486-8

Published electronically:
April 13, 2005

MathSciNet review:
2138137

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the Ricci flow becomes extinct in finite time on any Riemannian -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:
https://doi.org/10.1090/S0894-0347-05-00486-8

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