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