Preface
I look at the floor and I see it needs sweeping.
- Prom "While My Guitar Gently Weeps" by George Harrison of The Beatles
What Part II is about
Think the time is right for a palace revolution.
- Prom "Street Fighting Man" by Mick Jagger and Keith Richards of The
Rolling Stones
To help put the aim of this volume in perspective, we indulge in some
relative volume comparison (with apologies to Bishop and Gromov). Let
gij = ' The Ricci Flow: An Introduction' by two of the authors (through-
out this book we shall refer to this as 'Volume One' [142]), let T^ =
'Hamilton's Ricci Flow' by three of the authors [146],
let1
Rijki =F 'The
Ricci Flow: Techniques and Applications, Part I: Geometric Aspects' by
The Ricci
Flowers2
(throughout this book we shall refer to this as 'Part
I of this volume' [135]), let jftRijki
41
'The Ricci Flow: Techniques and
Applications, Part II: Analytic Aspects' (i.e., this book) by The Ricci Flow-
ers, and let ARijM = ' The Ricci Flow: Techniques and Applications, Part
III: Geometric-Analytic Aspects' (forthcoming) by The Ricci Flowers (we
shall refer to this as 'Part III of this volume'
[136]).3
Both g{j and T^
are introductory books, whereas the latter more comprehensive monographs
Rijki® §iRijki®^Rijkl are derived from the former. Finally, Volume Two
refers to the collection of Parts I, II, and III.
This is Part II, the sequel to Part I of this volume. In Rijki we discussed
various geometric topics in Ricci flow in more detail, such as Ricci solitons,
the Kahler-Ricci flow, the compactness theorem, Perelman's energy and
entropy monotonicity and the application to no local collapsing, the reduced
distance function and its application to the analysis of ancient solutions, and
finally a primer on 3-manifold topology.
We would like to than k Andrejs Treibergs and Junfang Li for suggesting the notation
Rijki-
Th e Ricci Flowers' is an abbreviation for the manifold/variety of authors of this
volume.
o
Th e originally intended two parts now comprise three parts.
ix
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