Holomorphic Maps and Invariant Distances
Elsevier (Publisher)
Published on 1. January 1980
225 pages
978-0-08-087151-6 (ISBN)
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Holomorphic Maps and Invariant Distances
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Tullio Franzoni | Edoardo Vesentini
Holomorphic Maps and Invariant Distances
Book
03/1980
Elsevier
€42.75
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Content
- Front Cover
- Holomorphic Maps and Invariant Distances
- Copyright Page
- Table of Contents
- Preface
- CHAPTER I. POLYNOMIALS AND POWER SERIES
- § 1. Multilinear maps and polynomials
- § 2. Convergent power series
- Notes
- CHAPTER II. HOLOMORPHIC FUNCTIONS
- § 1. Holomorphic functions
- § 2. The inverse mapping theorem
- § 3. Taylor expansion
- § 4. Gateaux holomorphy
- § 5. The Zorn theorem
- § 6. Plurisubharmonic and plurisuperharmonic functions
- Notes
- CHAPTER III. MAXIMUM PRINCIPLES
- § 1. A strong maximum principle
- § 2. A Schwarz lemma
- Notes
- CHAPTER IV. INVARIANT PSEUDODISTANCES
- § 1. The Kobayashi and Carathéodory pseudodistances
- § 2. Hyperbolic domains
- § 3. Local uniform convergence
- Notes
- CHAPTER V. INVARIANT DIFFERENTIAL METRICS
- § 1. The Kobayashi and Carathéodory differential metrics
- § 2. Local properties
- § 3. Inner distances
- § 4. The Kobayashi metric and the Kobayashi distance
- § 5. Application. A fixed point theorem
- § 6. Bounded domains in finitely dimensional vector spaces
- Notes
- CHAPTER VI. THE UNIT BALL IN A COMPLEX HILBERT SPACE
- § 1. Automorphisms of the unit ball
- § 2. Invariant distances and invariant metrics
- § 3. A linear representation of Aut(B)
- § 4. Holomorphic isometries and their fixed points
- Notes
- Appendix A: The Poincaré Metric
- Appendix B: Baire Spaces
- References
- Subject and Symbols Index
