Chapter 1. Hyperbolic geometry of the unit disc

Chapters in this book

1. Frontmatter i
2. Preface to the second edition vii
3. Preface to the first edition ix
4. Contents xi
5. Chapter 1. Hyperbolic geometry of the unit disc 1
6. Chapter 2. The Carathéodory pseudodistance and the Carathéodory–Reiffen pseudometric 20
7. Chapter 3. The Kobayashi pseudodistance and the Kobayashi–Royden pseudometric 106
8. Chapter 4. Contractible systems 150
9. Chapter 5. Properties of standard contractible systems 194
10. Chapter 6. Elementary Reinhardt domains 222
11. Chapter 7. Symmetrized polydisc 246
12. Chapter 8. Non-standard contractible systems 276
13. Chapter 9. Contractible functions and metrics for the annulus 329
14. Chapter 10. Elementary n-circled domains III 344
15. Chapter 11. Complex geodesics. Lempert’s theorem 358
16. Chapter 12. The Bergman metric 410
17. Chapter 13. Hyperbolicity 500
18. Chapter 14. Completeness 534
19. Chapter 15. Bergman completeness 573
20. Chapter 16. Complex geodesics – effective examples 592
21. Chapter 17. Analytic discs method 644
22. Chapter 18. Product property 667
23. Chapter 19. Comparison on pseudoconvex domains 691
24. Chapter 20. Boundary behavior of invariant functions and metrics on general domains 731
25. Appendix A. Miscellanea 765
26. Appendix B. Addendum 785
27. Appendix C. List of problems 809
28. Bibliography 814
29. List of symbols 844
30. Index 854