1547671870-The_Ricci_Flow__Chow

Mathematical Surveys and Monographs Volume 110 The Ricci Flow: An Introduction Bennett Chow Dan Knopf American Mathematical Soci ...

EDITORIAL COMMITTEE Jerry L. Bona Peter S. Landweber, Chair J. T. Stafford Michael P. Loss Tudor Stefan Ratiu 2000 Mathematics S ...

Contents Preface A guide for the reader A guide for the hurried reader Acknowledgments Chapter 1. The Ricci flow of special geom ...

iv CONTENTS ...

- Notes and commentary Chapter 5. The Ricci flow on surfaces l. The effect of a conformal change of metric Evolution of the ...

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Preface This book and its planned sequel(s) are intended to compose an introduc- tion to the Ricci flow in general and in partic ...

viii PREFACE model is a solution of the flow that arises as the limit of a sequence of dila- tions of an original solution appro ...

A GUIDE FOR THE READER ix heuristically. We also rigorously construct neckpinch solutions under certain symmetry assumptions. Th ...

x PREFACE derivative estimates established in this chapter enable one to prove the long- time existence theorem for the flow, wh ...

ACKNOWLEDGMENTS xi will be used in Section 6 of Chapter 9. The Harnack estimates for surfaces are prototypes of those that apply ...

x ii PREFACE The authors would also like to thank Sigurd Angenent, Albert Chau, Hsiao-Bing Cheng, Christine Guenther, Joel Hass, ...

CHAPTER 1 The Ricci flow of special geometries The Ricci flow 8 -g = -2Rc 8t g (0) =go and its cousin the normalized Ricci flow ...

2 1. THE RICCI FLOW OF SPECIAL GEOMETRIES REMARK 1.1. In dimension n = 3, the categories TOP, PL, and DIFF all coincide. In this ...

l. GEOMETRIZATION OF THREE-MANIFOLDS 3 REMARK 1.2. Seifert's original definition [116] of a fiber space required the existence o ...

4 1. THE RICCI FLOW OF SPECIAL GEOMETRIES N^3 is closed, irreducible, and homotopic to a hyperbolic 3-manifold, then N^3 is home ...

MODEL GEOMETRIES 5 on TxMn, one obtains a Yx-invariant scalar product gx by averaging §x un- der the action of Yx ".::=: g*. T ...

6 1. THE RICCI FLOW OF SPECIAL GEOMETRIES COROLLARY 1.11. ( 1) Given x, y E Mn and a linear isometry f: (TxMn, g (x))---+ (TyMn, ...

MAXIMAL MODEL GEOMETRIES 7 Signature Lie group Description (-1, -1, -1) SU (2) compact, simple (-1,-1,0) Isom ---------(JR.^2 ...

8 1. THE RICCI FLOW OF SPECIAL GEOMETRIES (a) M^3 is a Lie group isomorphic to SU (2); (b) M^3 is a Lie group isomorphic to ~^3 ...