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This volume contains the Proceedings of the International Workshop "Complex Analysis", which was held from February 12-16, 1990, in Wuppertal (Germany) in honour of H. Grauert, one of the most creative mathematicians in Complex Analysis of this century. In complete accordance with the width of the work of Grauert the book contains research notes and longer articles of many important mathematicians from all areas of Complex Analysis (Altogether there a re 49 articles in the volume). Some of the main subjects are: Cau chy-Riemann Equations with estimates, q-convexity, CR structures, deformation theory, envelopes of holomorphy, function algebras, complex group actions, Hodge theory, instantons, Kähler geometry, Lefschetz theorems, holomorphic mappings, Nevanlinna theory, com plex singularities, twistor theory, uniformization.
List of contents
Smooth Proper Modifications of Compact Kähler Manifolds.- Lp-Estimates for ?? in C.- Canonical Resolutions in Sheaves on Schubert and Brieskorn Varieties.- La forme hermitienne canonique pour une singularité presque isolée.- A Generalized Cousin Problem for Subvarieties of the Bidisk.- Scalar Curvature and Twistor Geometry.- Some Remarks on Weighted Estimates for ??.- Circular Models and Normal Forms for Convex Domains.- Lp-Estimates with Loss for the Bergman-Projection and the Canonical Solution to ??.- Distortion Function and the Heat Kernel of a Positive Line Bundle.- Twistor Spaces and Non-hyperbolicity of Certain Symplectic Kähler Manifolds.- Envelopes of Holomorphy of Domains in Cn.- Representing Measures in the Spectrum of H? (?).- Estimées Ck, ? pour l'equation ?? = f dans les convexes.- Local Hyperconvexity and Local Hyperconcavity.- Domaines à estimation maximale.- Deformation of Compact Rieman Surfaces with Distinguished Points.- Local Extension of Holomorphic L2-Functions with Weights.- On the Boundary Behavior of the Caratheodory and Kobayashi Distances in Strongly Pseudoconvex Domains in Cn.- Zur Klassifikation der 1-konvexen komplexen Räume.- Holomorphic Mappings into Convex Domains.- On Second Order Hypoelliptic Differential Operators and the ??-Neumann Problem.- Equisingularity of Analytically Constructible Sets.- Fonction de Artin d'un germe d'espace analytique.- Local Peaks Sets and Maximum Modulus Sets in Products of Strictly Pseudoconvex Domains.- Hyperbolic C* -Actions on Affine Surfaces.- On Complex Manifolds Exhausted by Biholomorphic Images of Generalized Complex Ellipsoids E(n; n1,@@@, ns; p1,@@@, ps).- The Hard Lefschetz Theorem for Concave and Convex Algebraic Manifolds.- Sur la résolution des équations deCauchy-Riemann tangentielles pour les formes à support compact dans les variétes.- Imbedding Pseudohermitian Manifolds into a Sphere.- Deformations of Strongly Pseudo-Convex CR Structures and Deformations of Normal Isolated Singularities.- The Behavior of Multiplier Ideal Sheaves under Morphisms.- Local Geometry of Decoupled Pseudoconvex Domains.- A Vanishing Theorem on Kähler Manifolds with Certain Stratified Structures.- Hodge-Kohomologie und Steinsche Mannigfaltigkeiten.- The Cauchy-Riemann Equations in Convex Domains.- Integral Kernels and Hölder Estimates for ?? on Pseudoconvex Domains of Finite Type on C2.- Complex Analysis in the Golden Fifties.- On q-Convex Exhaustion Functions of Complements of CR-Submanifolds.- A Characterization of Homogeneous Bounded Domains.- Singular Sets of Separately Analytic Functions.- Some Recent Results Related to the Uniformization Problem in Several Complex Variables.- Product Decomposition of Non-reduced Space Germs.- Modular Subgerms and the Isomorphism Problem in Deformation Theory.- A New Method to Introduce a-priori Estimates for the ??-Neumann Problem.- Maximal and Semi-Maximal Estimates for ??b on Pseudoconvex Manifolds.- Degenerations of Instantons.- Second Main Theorems in Number Theory and Nevanlinna Theory.- Symplectic Techniques in Holomorphic Group Actions.
