[بخش سوم: جنبه‌های هندسی-تحلیلی] جریان ریچی: تکنیک‌ها و کاربردها

This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kahler-Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results. This book gives a presentation of topics in Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject. The authors have aimed at presenting technical material in a clear and detailed manner. In this volume, geometric aspects of the theory have been emphasized. The book presents the theory of Ricci solitons, Kähler–Ricci flow, compactness theorems, Perelman's entropy monotonicity and no local collapsing, Perelman's reduced distance function and applications to ancient solutions, and a primer of 3-manifold topology. Various technical aspects of Ricci flow have been explained in a clear and detailed manner. The authors have tried to make some advanced material accessible to graduate students and nonexperts. The book gives a rigorous introduction to Perelman's work and explains technical aspects of Ricci flow useful for singularity analysis. Throughout, there are appropriate references so that the reader may further pursue the statements and proofs of the various results. Contents Preface Contents of Part III of Volume Two Notation and Symbols Chapter 17. Entropy, $\mu$-invariant, and Finite Time Singularities Chapter 18. Geometric Tools and Point Picking Methods Chapter 19. Geometric Properties of $\kappa$-Solutions Chapter 20. Compactness of the Space of $\kappa$-Solutions Chapter 21. Perelman's Pseudolocality Theorem Chapter 22. Tools Used in Proof of Pseudolocality Chapter 23. Heat Kernel for Static Metrics Chapter 24. Heat Kernel for Evolving Metrics Chapter 25. Estimates of the Heat Equation for Evolving Metrics Chapter 26. Bounds for the Heat Kernel for Evolving Metrics Appendix G. Elementary Aspects of Metric Geometry Appendix H. Convex Functions on Riemannian Manifolds Appendix I. Asymptotic Cones and Sharafutdinov Retraction Appendix J. Solutions to Selected Exercises Bibliography Index Pt. 1. Geometric Aspects -- Pt. 2. Analytic Aspects -- Pt. 3. Geometric-analytic Aspects -- Pt.4 Long-time Solutions And Related Topics. Bennett Chow ... [et Al.]. Includes Bibliographical References And Index.