Self-contained book on Ricci Flow/Geometric Analysis Can someone please tell me whether there is any self-contained book on Geometric Analysis/Ricci Flow/analytic techniques used in Riemannian Geometry? By self-contained I mean it does not assume that the reader is familiar with Analysis of PDE, rather quotes the required results and have a comprehensive appendix on PDE. I would appreciate if the book contained some exercises also.
 A: A quick search on Amazon provides at least three titles that are introductory texts to the topic for graduate students.
(1) B. Chow, P. Lu, L. Ni: Hamilton's Ricci Flow, Graduate Studies in Mathematics 77, AMS 2006;
(2) B. Chow, D. Knopf: The Ricci Flow: An Introduction, Mathematical Surveys and Monographs 110, AMS 2004;
(3) B. Chow and others: The Ricci Flow: Techniques and Applications: Geometric Aspects, Mathematical Surveys and Monographs 135, AMS 2007.
A: These books may also be the sort of thing you are after:


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*Peter Topping, Lectures on the Ricci flow

*Ben Andrews and Christopher Hopper, Ricci Flow in Riemannian Geometry A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem


As Dean Yang pointed out in the comments above, being a PDE, the Ricci flow is, not surprisingly, studied by PDE methods. However, you can make a reasonable start far with only knowledge of the maximum principle (it's even described in Topping's book) if your are willing to assume existence/uniqueness. I think each book is fairly self-contained, and while many techniques used are PDE techniques, you can probably read them without knowing they apply to a broader range of PDE.
