Here is a list of literature which I compiled when I taught the course on Ricci flow.
Basic differential geometry:
Einstein Manifolds (Besse).
Riemannian geometry (Gallot S., Hulin D., Lafontaine J.)
Sign and geometric meaning of curvature (Gromov)
http://www.ihes.fr/~gromov/PDF/1%5B77%5D.pdf
- Einstein Manifolds (Besse).
- Riemannian geometry (Gallot S., Hulin D., Lafontaine J.)
- Sign and geometric meaning of curvature (Gromov), also available here
Textbooks:
Lectures on the Ricci Flow (2006, 133 pp.) Topping P.
http://www.warwick.ac.uk/~maseq/RFnotes.html
Hamilton's Ricci Flow (Chow B., Lu P., Ni L.)
- Lectures on the Ricci Flow (2006, 133 pp.) Topping P.
- Hamilton's Ricci Flow (Chow B., Lu P., Ni L.)
Standard texts:
http://en.wikipedia.org/wiki/Solution_of_the_Poincar%C3%A9_conjecture
(and links therein)
Perelman, Grisha (November 11, 2002).
The entropy formula for the Ricci flow and its geometric applications.
Perelman, Grisha (March 10, 2003).
Ricci flow with surgery on three-manifolds.
Perelman, Grisha (July 17, 2003).
Finite extinction time for the solutions to the
Ricci flow on certain three-manifolds.
Bruce Kleiner, John Lott. Notes on Perelman's papers
Huai-Dong Cao, Xi-Ping Zhu. Hamilton-Perelman's Proof of
the Poincaré Conjecture and the Geometrization Conjecture.
John W. Morgan, Gang Tian.
Ricci Flow and the Poincaré Conjecture
Wikipedia: Poincaré conjecture (and links therein)
Perelman, Grisha (November 11, 2002).
The entropy formula for the Ricci flow and its geometric applications.Perelman, Grisha (March 10, 2003). Ricci flow with surgery on three-manifolds.
Perelman, Grisha (July 17, 2003). Finite extinction time for the solutions to the Ricci flow on certain three-manifolds.
Bruce Kleiner, John Lott. Notes on Perelman's papers
Huai-Dong Cao, Xi-Ping Zhu. Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture.
John W. Morgan, Gang Tian. Ricci Flow and the Poincaré Conjecture
It's very obsolete (2007), and does not contain much on short-term existence of solutions of Ricci flow.
