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Intro; Preface; Contents; On a Hyperconvex Manifold Without Non-constant Bounded Holomorphic Functions; 1 Introduction; 2 Grauert Tube and Its Hyperconvexity; 3 Proofs of the Liouville Property; 4 Open Problems; References; CR-Geometry and Shearfree Lorentzian Geometry; 1 Subconformal and CR-Manifolds; 2 Shearfree Congruences; 3 Shearfree Congruences and Their Orbit Spaces; 4 Applications of Shearfree Congruences in Dimension 4; References; Complex Surfaces with Many Holomorphic Automorphisms; 1 Automorphisms of Complex-Euclidean Space; 2 Density Property; 3 Quasi-Homogeneous Surfaces
4 Open QuestionsReferences; Fatou Components for Conservative Holomorphic Surface Automorphisms; 1 Introduction; 2 Fatou Set of a Conservative Hénon Map; 3 Rotation Domains; 4 Reinhardt Domains; 5 Existence of Rotation Domains; 6 Nonexistence of Rotation Domains; 7 Computer Pictures: The Ushiki Approach; 8 Herman Rings for Dissipative Maps?; 9 Rational Surface Automorphisms Preserving a 2-Form; References; A Twistor Transform for the Kobayashi Metric on a Convex Domain; 1 Introduction; 2 Kobayashi Disks; 3 Statement of Results; 4 The Standard Model; 4.1 The Space X; 4.2 The Tangent Space TxX
2 Prelimiaries2.1 The Kähler-Einstein Metric on a Strongly Pseudoconvex Domain; 2.2 Horizontal Lifts and Geodesic Curvatures; 3 The Geodesic Curvature of the Real (1,1)-Form Defined by a Defining Function; 4 Variation of Bounded Strongly Pseudoconvex Domains; 5 Variation of Bounded Pseudoconvex Domains; 5.1 Kähler-Einstein Metric on a Bounded Pseudoconvex Domain; 5.2 Plurisubharmonicity of the Variation; 6 Local Trivility; References; Extension of Holomorphic Functions and Cohomology Classes from Non Reduced Analytic Subvarieties; 1 Introduction and Main Results
2 Bochner-Kodaira Estimate with Approximation3 Sketch of Proof of the Extension Theorem; 4 Applications of the Ohsawa-Takegoshi Extension Theorem; 4.1 Approximation of Plurisubharmonic Functions and of Closed (1,1)-Currents; 4.2 Invariance of Plurigenera; 4.3 Semicontinuity of Log Singularity Exponents; 4.4 Proof of the Suita Conjecture; References; Group Actions in Several Complex Variables: A Survey; 1 Automorphism Groups of Special Invariant Domains; 2 Rigidity of Automorphism Groups of Certain Invariant Domains; 3 Orbit Convexity
4 Open QuestionsReferences; Fatou Components for Conservative Holomorphic Surface Automorphisms; 1 Introduction; 2 Fatou Set of a Conservative Hénon Map; 3 Rotation Domains; 4 Reinhardt Domains; 5 Existence of Rotation Domains; 6 Nonexistence of Rotation Domains; 7 Computer Pictures: The Ushiki Approach; 8 Herman Rings for Dissipative Maps?; 9 Rational Surface Automorphisms Preserving a 2-Form; References; A Twistor Transform for the Kobayashi Metric on a Convex Domain; 1 Introduction; 2 Kobayashi Disks; 3 Statement of Results; 4 The Standard Model; 4.1 The Space X; 4.2 The Tangent Space TxX
2 Prelimiaries2.1 The Kähler-Einstein Metric on a Strongly Pseudoconvex Domain; 2.2 Horizontal Lifts and Geodesic Curvatures; 3 The Geodesic Curvature of the Real (1,1)-Form Defined by a Defining Function; 4 Variation of Bounded Strongly Pseudoconvex Domains; 5 Variation of Bounded Pseudoconvex Domains; 5.1 Kähler-Einstein Metric on a Bounded Pseudoconvex Domain; 5.2 Plurisubharmonicity of the Variation; 6 Local Trivility; References; Extension of Holomorphic Functions and Cohomology Classes from Non Reduced Analytic Subvarieties; 1 Introduction and Main Results
2 Bochner-Kodaira Estimate with Approximation3 Sketch of Proof of the Extension Theorem; 4 Applications of the Ohsawa-Takegoshi Extension Theorem; 4.1 Approximation of Plurisubharmonic Functions and of Closed (1,1)-Currents; 4.2 Invariance of Plurigenera; 4.3 Semicontinuity of Log Singularity Exponents; 4.4 Proof of the Suita Conjecture; References; Group Actions in Several Complex Variables: A Survey; 1 Automorphism Groups of Special Invariant Domains; 2 Rigidity of Automorphism Groups of Certain Invariant Domains; 3 Orbit Convexity