Details

Autor(en) / Beteiligte

• Franzoni, Tullio,
• Vesentini, Edoardo

Titel

Holomorphic maps and invariant distances [electronic resource]

Link zum Volltext

• Elsevier Books AutoHoldings

Beschreibungen/Notizen

• "These notes originate from lectures given at the University of Maryland and at the Scuola normale superiore, Pisa, in the past two years."
• Includes bibliographical references (p. 211-223) and index.
• 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
• Holomorphic maps and invariant distances
• English