CHAPTER 7. The Comparison Theorem

Chapters in this book

1. Frontmatter i
2. Table of Contents v
3. Acknowledgments ix
4. CHAPTER 1. Introduction 1
5. Part I. Preliminary Results in 2- and 3-Dimensional Riemannian Geometry
6. CHAPTER 2. Generalized Hodge Systems in 2-D 31
7. CHAPTER 3. General Results in 3-D Geometry 53
8. CHAPTER 4. The Poisson Equation in 3-D 78
9. CHAPTER 5. Curvature of an Initial Data Set 110
10. CHAPTER 6. Deformation of 2-Surfaces in 3-D 121
11. Part II. Bianchi Equations in Space-Time
12. CHAPTER 7. The Comparison Theorem 135
13. CHAPTER 8. The Error Estimates 205
14. Part III. Construction of Global Space- Times. Proof of the Main Theorem
15. CHAPTER 9. Construction of the Optical Function 261
16. CHAPTER 10. Third Version of the Main Theorem 284
17. CHAPTER 11. Second Fundamental Form 311
18. CHAPTER 12. The Lapse Function 341
19. CHAPTER 13. Derivatives of the Optical Function 351
20. CHAPTER 14. The Last Slice 411
21. CHAPTER 15. The Matching 443
22. CHAPTER 16. The Rotation Vectorfields 466
23. CHAPTER 17. Conclusions 491
24. Bibliography 513