Book contents
- Frontmatter
- Contents
- Introduction
- 1 Elementary transformations of the Euclidean plane and the Riemann sphere
- 2 Hyperbolic metric in the unit disk
- 3 Holomorphic functions
- 4 Topology and uniformization
- 5 Discontinuous groups
- 6 Fuchsian groups
- 7 The hyperbolic metric for arbitrary domains
- 8 The Kobayashi metric
- 9 The Carathéodory pseudo-metric
- 10 Inclusion mappings and contraction properties
- 11 Applications I: forward random holomorphic iteration
- 12 Applications II: backward random iteration
- 13 Applications III: limit functions
- 14 Estimating hyperbolic densities
- 15 Uniformly perfect domains
- 16 Appendix: a brief survey of elliptic functions
- Bibliography
- Index
2 - Hyperbolic metric in the unit disk
Published online by Cambridge University Press: 13 January 2010
Book contents
- Frontmatter
- Contents
- Introduction
- 1 Elementary transformations of the Euclidean plane and the Riemann sphere
- 2 Hyperbolic metric in the unit disk
- 3 Holomorphic functions
- 4 Topology and uniformization
- 5 Discontinuous groups
- 6 Fuchsian groups
- 7 The hyperbolic metric for arbitrary domains
- 8 The Kobayashi metric
- 9 The Carathéodory pseudo-metric
- 10 Inclusion mappings and contraction properties
- 11 Applications I: forward random holomorphic iteration
- 12 Applications II: backward random iteration
- 13 Applications III: limit functions
- 14 Estimating hyperbolic densities
- 15 Uniformly perfect domains
- 16 Appendix: a brief survey of elliptic functions
- Bibliography
- Index
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- Hyperbolic Geometry from a Local Viewpoint , pp. 32 - 52Publisher: Cambridge University PressPrint publication year: 2007