Linked e-resources
Details
Table of Contents
Stein Manifolds and Holomorphic Mappings; Preface to the Second Edition; Preface to the First Edition; Contents; Part I: Stein Manifolds; Chapter 1: Preliminaries; 1.1 Complex Manifolds and Holomorphic Maps; 1.2 Examples of Complex Manifolds; 1.3 Subvarieties and Complex Spaces; 1.4 Holomorphic Fibre Bundles; 1.5 Holomorphic Vector Bundles; 1.6 The Tangent Bundle; 1.7 The Cotangent Bundle and Differential Forms; 1.8 Plurisubharmonic Functions and the Levi Form; 1.9 Vector Fields, Flows and Foliations; 1.10 What is the H-Principle?; Chapter 2: Stein Manifolds; 2.1 Domains of Holomorphy
2.2 Stein Manifolds and Stein Spaces2.3 Holomorphic Convexity and the Oka-Weil Theorem; 2.4 Embedding Stein Manifolds into Euclidean Spaces; 2.5 Characterization by Plurisubharmonic Functions; 2.6 Cartan-Serre Theorems A & B; 2.7 The -Problem; 2.8 Cartan-Oka-Weil Theorem with Parameters; Chapter 3: Stein Neighborhoods and Approximation; 3.1 Q-Complete Neighborhoods; 3.2 Stein Neighborhoods of Stein Subvarieties; 3.3 Holomorphic Retractions onto Stein Submanifolds; 3.4 A Semiglobal Holomorphic Extension Theorem; 3.5 Approximation on Totally Real Submanifolds
3.6 Stein Neighborhoods of Laminated Sets3.7 Stein Compacts with Totally Real Handles; 3.8 A Mergelyan Approximation Theorem; 3.9 Strongly Pseudoconvex Handlebodies; 3.10 Morse Critical Points of q-Convex Functions; 3.11 Critical Levels of a q-Convex Function; 3.12 Topological Structure of a Stein Space; Chapter 4: Automorphisms of Complex Euclidean Spaces; 4.1 Shears; 4.2 Automorphisms of C2; 4.3 Attracting Basins and Fatou-Bieberbach Domains; 4.4 Random Iterations and the Push-Out Method; 4.5 Mittag-Lef er Theorem for Entire Maps; 4.6 Tame Discrete Sets in Cn
4.7 Unavoidable and Rigid Discrete Sets4.8 Algorithms for Computing Flows; 4.9 The Andersén-Lempert Theory; 4.10 The Density Property; 4.11 Automorphisms Fixing a Subvariety; 4.12 Moving Polynomially Convex Sets; 4.13 Moving Totally Real Submanifolds; 4.14 Carleman Approximation by Automorphisms; 4.15 Automorphisms with Given Jets; 4.16 Mittag-Lef er Theorem for Automorphisms of Cn; 4.17 Interpolation by Fatou-Bieberbach Maps; 4.18 Twisted Holomorphic Embeddings into Cn; 4.19 Nonlinearizable Periodic Automorphisms of Cn; 4.20 A Non-Runge Fatou-Bieberbach Domain
4.21 A Long C2 Without Holomorphic FunctionsPart II: Oka Theory; Chapter 5: Oka Manifolds; 5.1 A Historical Introduction to the Oka Principle; 5.2 Cousin Problems and Oka's Theorem; 5.3 The Oka-Grauert Principle; 5.4 What is an Oka Manifold?; 5.5 Basic Properties of Oka manifolds; 5.6 Examples of Oka Manifolds; 5.7 Cartan Pairs; 5.8 A Splitting Lemma; 5.9 Gluing Holomorphic Sprays; 5.10 Noncritical Strongly Pseudoconvex Extensions; 5.11 Proof of Theorem 5.4.4: The Basic Case; 5.12 Proof of Theorem 5.4.4: Strati ed Fibre Bundles; 5.13 Proof of Theorem 5.4.4: The Parametric Case
2.2 Stein Manifolds and Stein Spaces2.3 Holomorphic Convexity and the Oka-Weil Theorem; 2.4 Embedding Stein Manifolds into Euclidean Spaces; 2.5 Characterization by Plurisubharmonic Functions; 2.6 Cartan-Serre Theorems A & B; 2.7 The -Problem; 2.8 Cartan-Oka-Weil Theorem with Parameters; Chapter 3: Stein Neighborhoods and Approximation; 3.1 Q-Complete Neighborhoods; 3.2 Stein Neighborhoods of Stein Subvarieties; 3.3 Holomorphic Retractions onto Stein Submanifolds; 3.4 A Semiglobal Holomorphic Extension Theorem; 3.5 Approximation on Totally Real Submanifolds
3.6 Stein Neighborhoods of Laminated Sets3.7 Stein Compacts with Totally Real Handles; 3.8 A Mergelyan Approximation Theorem; 3.9 Strongly Pseudoconvex Handlebodies; 3.10 Morse Critical Points of q-Convex Functions; 3.11 Critical Levels of a q-Convex Function; 3.12 Topological Structure of a Stein Space; Chapter 4: Automorphisms of Complex Euclidean Spaces; 4.1 Shears; 4.2 Automorphisms of C2; 4.3 Attracting Basins and Fatou-Bieberbach Domains; 4.4 Random Iterations and the Push-Out Method; 4.5 Mittag-Lef er Theorem for Entire Maps; 4.6 Tame Discrete Sets in Cn
4.7 Unavoidable and Rigid Discrete Sets4.8 Algorithms for Computing Flows; 4.9 The Andersén-Lempert Theory; 4.10 The Density Property; 4.11 Automorphisms Fixing a Subvariety; 4.12 Moving Polynomially Convex Sets; 4.13 Moving Totally Real Submanifolds; 4.14 Carleman Approximation by Automorphisms; 4.15 Automorphisms with Given Jets; 4.16 Mittag-Lef er Theorem for Automorphisms of Cn; 4.17 Interpolation by Fatou-Bieberbach Maps; 4.18 Twisted Holomorphic Embeddings into Cn; 4.19 Nonlinearizable Periodic Automorphisms of Cn; 4.20 A Non-Runge Fatou-Bieberbach Domain
4.21 A Long C2 Without Holomorphic FunctionsPart II: Oka Theory; Chapter 5: Oka Manifolds; 5.1 A Historical Introduction to the Oka Principle; 5.2 Cousin Problems and Oka's Theorem; 5.3 The Oka-Grauert Principle; 5.4 What is an Oka Manifold?; 5.5 Basic Properties of Oka manifolds; 5.6 Examples of Oka Manifolds; 5.7 Cartan Pairs; 5.8 A Splitting Lemma; 5.9 Gluing Holomorphic Sprays; 5.10 Noncritical Strongly Pseudoconvex Extensions; 5.11 Proof of Theorem 5.4.4: The Basic Case; 5.12 Proof of Theorem 5.4.4: Strati ed Fibre Bundles; 5.13 Proof of Theorem 5.4.4: The Parametric Case