Summary: RESEARCH BLOG 4/29/03
Last Wednesday, Dan Knopf visited from University of Iowa. He
was a graduate student at Wisconsin, but was unofficially a student of
Bennett Chow. Together they are writing a monograph on Hamilton's
program for solving geometrization using Ricci flow (see blog 2/26/03).
He has an unfinished copy (which is already 233 pages), but the first
volume will not be finished until the end of this year. If you are inter-
ested in proof reading it, you can contact Dan, but he is not distributing
it any more on his web page. I'll list the chapter topics:
1. Ricci flow for special geometries: this computes the Ricci flow for
homogeneous geometries on 3-manifolds.
2. Special and limit solutions: this describes soliton solutions and
what one expects certain solutions to look like, such as eternal and
ancient solutions and neck pinches.
3. Short-time existence: they follow DeTurck's trick to show short-
time existence for the Ricci flow, by finding a related equation
which is strictly parabolic. Hamilton has a modified version in
his paper on formation of singularities, which is more conceptually
clear using harmonic maps, but they only sketch this argument.
4. Weak maximum principles: a key idea of Hamilton's is a matrix