Mathematics > Differential Geometry
Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
Grisha Perelman
(Submitted on 17 Jul 2003)
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.