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

@article{Colding2003EstimatesFT, title={Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman}, author={T. Colding and W. Minicozzi}, journal={Journal of the American Mathematical Society}, year={2003}, volume={18}, pages={561-569} }

We show that the Ricci flow becomes extinct in finite time on any Riemannian 3-manifold without aspherical summands. In this note we prove some bounds for the extinction time for the Ricci flow on certain 3-manifolds. Our interest in this comes from a question that Grisha Perelman asked the first author at a dinner in New York City on April 25th of 2003. His question was "what happens to the Ricci flow on the 3-sphere when one starts with an arbitrary metric? In particular, does the flow become… Expand

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Finite extinction time for the solutions to the Ricci flow on certain three-manifolds

- Mathematics
- 2003

Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes

- Mathematics
- 1988