Invariant Distances and Metrics in Complex Analysis
1st Edition
Published on 3. May 2011
XI, 408 pages
978-3-11-087031-2 (ISBN)
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Marek Jarnicki | Peter Pflug
Invariant Distances and Metrics in Complex Analysis
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Marek Jarnicki | Peter Pflug
Invariant Distances and Metrics in Complex Analysis
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Marek Jarnicki | Peter Pflug
Invariant Distances and Metrics in Complex Analysis
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01/1993
1st Edition
De Gruyter
€239.00
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Content
- Intro
- Preface
- I Hyperbolic geometry of the unit disc
- Exercises
- II The Carathéodory pseudodistance and the Carathéodory-Reiffen pseudometric
- 2.1 Definitions. General Schwarz-Pick Lemma
- 2.2 Balanced domains
- 2.3 Carathéodory hyperbolicity
- 2.4 The Carathéodory topology
- 2.5 Properties of c(*)and ?. Length of curve. Inner Carathéodory pseudodistance
- 2.6 Two applications
- 2.7 A class of n-circled domains
- Notes
- Exercises
- III The Kobayashi pseudodistance and the Kobayashi-Royden pseudometric
- 3.1 The Lempert function and the Kobayashi pseudodistance
- 3.2 Tautness
- 3.3 General properties of k
- 3.4 An extension theorem
- 3.5 The Kobayashi-Royden pseudometric
- 3.6 The Kobayashi-Buseman pseudometric
- 3.7 Product-formula
- Notes
- Exercises
- IV Contractible systems
- 4.1 Abstract point of view
- 4.2 Extremal problems for plurisubharmonic functions
- 4.3 Inner pseudodistances. Integrated forms. Derivatives. Buseman pseudometrics. C1-pseudodistances
- 4.4 Example - elementary n-circled domains
- Notes
- Exercises
- V Contractible functions and metrics for the annulus
- Notes
- Exercises
- VI The Bergman metric
- 6.1 The Bergman kernel
- 6.2 The Bergman pseudometric
- 6.3 Comparison and localization
- 6.4 The Skwarczynski pseudometric
- Notes
- Exercises
- VII Hyperbolicity and completeness
- 7.1 Global hyperbolicity
- 7.2 Local hyperbolicity
- 7.3 Completeness - general discussion
- 7.4 Carathéodory completeness
- 7.5 Kobayashi completeness
- 7.6 Bergman completeness
- Notes
- Exercises
- VIII Complex geodesics. Lempert's theorem
- 8.1 Complex geodesics
- 8.2 Lempert's theorem
- 8.3 Uniqueness of complex geodesies
- 8.4 Geodesics in convex complex ellipsoids
- 8.5 Biholomorphisms of complex ellipsoids
- 8.6 Schwarz Lemma - the case of equality
- 8.7 Criteria for biholomorphicity
- Notes
- Exercises
- IX Product-property
- Exercises
- X Comparison on strongly pseudoconvex domains
- 10.1 Strongly pseudoconvex domains
- 10.2 The boundary behavior of the Carathéodory and the Kobayashi distances
- 10.3 Localization
- 10.4 Boundary behavior of the Carathéodory-Reiffen and the Kobayashi-Royden metrics
- 10.5 A comparison of distances
- 10.6 Characterization of the unit ball by its automorphism group
- Notes
- Exercises
- Miscellanea
- A The automorphism group of bounded domains
- B Holomorphic curvature
- C Complex geodesics
- D Criteria for biholomorphicity
- E Boundary behavior of contractible metrics on weakly pseudoconvex domains
- Appendix
- HF Holomorphic functions
- PSH Subharmonic and plurisubharmonic functions
- PSC Domains of holomorphy and pseudoconvex domains
- AUT Automorphisms
- Automorphisms of the unit disc
- Automorphisms of the unit polydisc
- Automorphisms of the unit Euclidean ball
- GR Green function and Dirichlet problem
- MA Monge-Ampère operator
- H Hardy spaces
- References
- List of symbols
- Index
