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

Grisha Perelman
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Abstract

Let M be a closed oriented three-manifold, whose prime decomposition contains no aspherical factors. We show that for any initial riemannian metric on M the solution to the Ricci flow with surgery, defined in our previous paper math.DG/0303109, becomes extinct in finite time. The proof uses a version of the minimal disk argument from 1999 paper by Richard Hamilton, and a regularization of the curve shortening flow, worked out by Altschuler and Grayson.

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Grisha Perelman. 2003-07-17. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds. https://arxiv.org/abs/math/0307245

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