Holomorphic Maps and Invariant Distances (eBook)

eBook Download: PDF

1980 | 1. Auflage
225 Seiten
Elsevier Science (Verlag)
978-0-08-087151-6 (ISBN)

Infos

Holomorphic maps and invariant distances

Inhalt

Front Cover 1
Holomorphic Maps and Invariant Distances 4
Copyright Page 5
Table of Contents 8
Preface 6
CHAPTER I. POLYNOMIALS AND POWER SERIES 10
§ 1. Multilinear maps and polynomials 10
§ 2. Convergent power series 24
Notes 34
CHAPTER II. HOLOMORPHIC FUNCTIONS 36
§ 1. Holomorphic functions 36
§ 2. The inverse mapping theorem 41
§ 3. Taylor expansion 47
§ 4. Gateaux holomorphy 54
§ 5. The Zorn theorem 65
§ 6. Plurisubharmonic and plurisuperharmonic functions 71
Notes 74
CHAPTER III. MAXIMUM PRINCIPLES 76
§ 1. A strong maximum principle 76
§ 2. A Schwarz lemma 84
Notes 88
CHAPTER IV. INVARIANT PSEUDODISTANCES 90
§ 1. The Kobayashi and Carathéodory pseudodistances 90
§ 2. Hyperbolic domains 100
§ 3. Local uniform convergence 107
Notes 118
CHAPTER V. INVARIANT DIFFERENTIAL METRICS 122
§ 1. The Kobayashi and Carathéodory differential metrics 122
§ 2. Local properties 130
§ 3. Inner distances 137
§ 4. The Kobayashi metric and the Kobayashi distance 141
§ 5. Application. A fixed point theorem 146
§ 6. Bounded domains in finitely dimensional vector spaces 148
Notes 152
CHAPTER VI. THE UNIT BALL IN A COMPLEX HILBERT SPACE 154
§ 1. Automorphisms of the unit ball 154
§ 2. Invariant distances and invariant metrics 162
§ 3. A linear representation of Aut(B) 173
§ 4. Holomorphic isometries and their fixed points 183
Notes 192
Appendix A: The Poincaré Metric 194
Appendix B: Baire Spaces 210
References 220
Subject and Symbols Index 234

Produkt-Details

• Erscheint lt. Verlag: 1.1.1980
• Mitarbeit: Herausgeber (Serie): Leopoldo Nachbin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-087151-8 / 0080871518
• ISBN-13: 978-0-08-087151-6 / 9780080871516