《Hamilton曲率流》是由美國數學家Bennett Chow、Peng Lu與Lei Ni合著的數學專著，2006年12月由科學出版社出版第1版英文專著，歸屬於《當代數學講座叢書》。該書以Hamilton的幾何化猜想研究計畫為背景，闡述Ricci流理論在三維流形拓撲分類中的套用，並涵蓋Perelman在該領域的成果。
全書內容包括Ricci流的基礎理論，如黎曼幾何初步、曲率流方程解的特性、奇異點分析方法及高維非緊流形中的拓展套用。通過孤立子解、等周估計等專題，介紹從經典結論到前沿進展的內容。附錄部分補充了幾何分析與偏微分方程技術方法。
基本介紹
- 中文名：Hamilton曲率流
- 作者：Bennett Chow、Peng Lu, Lei Ni
- 出版社：科學出版社
- 出版時間：2006-12
- ISBN：7030177991
內容簡介,圖書目錄,
內容簡介
We give a quick introduction to Ricci flow. Ricci flow is currently a hot topic in mathematics. Its development over the last two decades has primarily been aimed at understanding the Geometrization Conjecture. Recently Perelman has made spectacular progress on Hamilton's well-developed program aimed at proving the Geometrization and Poincare Conjectures. Our book will quickly lead the reader through much of the basic material in the subject up to some of the most recent developments.
圖書目錄
Preface
Acknowledgments
A Detailed Guide for the Reader
Notation and Symbols
Chapter 1. Riemannian Geometry
Chapter 2. Fundamentals of the Ricci Flow Equation
Chapter 3. Closed 3-manifolds with Positive Ricci Curvature
Chapter 4. Ricci Solitons and Special Solutions
Chapter 5. Isoperimetric Estimates and No Local Collapsing
Chapter 6. Preparation for Singularity Analysis
Chapter 7. High-dimensional and Noncompact Ricci Flow
Chapter 8. Singularity Analysis
Chapter 9. Ancient Solutions
Chapter 10. Differential Harnack Estimates
Chapter 11. Space-time Geometry
Appendix A. Geometric Analysis Related to Ricci Flow
Appendix B. Analytic Techniques for Geometric Flows
Appendix S. Solutions to Selected Exercises
Bibliography
Index
