Width and finite extinction time of Ricci flow
Tobias H. Colding, William P. Minicozzi II,
2007.07.01
http://arxiv.org/abs/0707.0108
This is an expository article with complete proofs intended for a general
nonspecialist audience. The results are twofold. First, we discuss a
geometric invariant, that we call the width, of a manifold and show how it can
be realized as the sum of areas of minimal 2spheres. For instance, when $M$ is
a homotopy 3sphere, the width is loosely speaking the area of the smallest
2sphere needed to ``pull over'' $M$. Second, we use this to conclude that
Hamilton's Ricci flow becomes extinct in finite time on any homotopy 3sphere.
We have chosen to write this since the results and ideas given here are quite
useful and seem to be of interest to a wide audience.
