Complex Analysis: Proceedings of the International Workshop Wuppertal 1990 (Aspects of Mathematics, 1)

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. Front Matter....Pages I-IX Smooth proper modifications of compact Kähler manifolds....Pages 1-7 L p -Estimates for ∂̄ in C....Pages 8-13 Canonical resolutions of sheaves on Schubert and Brieskorn varieties....Pages 14-19 La forme hermitienne canonique pour une singularité presque isolée....Pages 20-28 A generalized Cousin problem for subvarieties of the bidisk....Pages 29-32 Scalar Curvature and Twistor Geometry....Pages 33-39 Some Remarks on weighted Estimates for ∂̄....Pages 40-43 Circular Models and Normal Forms for Convex Domains....Pages 44-51 L p -Estimates with Loss for the Bergman Projection and the Canonical Solution to ∂̄....Pages 52-59 Distortion Function and the Heat Kernel of a Positive Line Bundle....Pages 60-63 Twistor spaces and non-hyperbolicity of certain symplectic Kähler manifolds....Pages 64-69 Envelopes of Holomorphy of Domains in C n ....Pages 70-76 Representing Measures in the Spectrum of H ∞ (Ω)....Pages 77-80 Estimées C k, α pour l’equation ∂̄ u = f dans les convexes....Pages 81-88 Local hyperconvexity and local hyperconcavity....Pages 89-91 Domaines a estimation maximale....Pages 92-100 Deformation of Compact Riemann Surfaces with Distinguished Points....Pages 101-105 Local Extension of Holomorphic L 2 -Functions with Weights....Pages 106-110 On the Boundary Behavior of the Caratheodory and Kobayashi Distances in Strongly Pseudoconvex Domains in C n ....Pages 111-114 Zur Klassifikation der 1-konvexen komplexen Räume....Pages 115-126 Holomorphic Mappings into Convex Domains....Pages 127-133 On second order hypoelliptic differential operators and the ∂̄-Neumann problem....Pages 134-142 Equisingularity of Analytically Constructible Sets....Pages 143-147 Fonction de Artin d’un germe d’espace analytique....Pages 148-154 Local Peak Sets and Maximum Modulus Sets in Products of Strictly Pseudoconvex Domains....Pages 155-159 Hyperbolic C*-Actions on Affine Algebraic Surfaces....Pages 160-168 On complex manifolds exhausted by biholomorphic images of generalized complex ellipsoids $$\mathbb{E}$$ (n;n 1 , ... , n s ;p 1 , ... , p s )....Pages 169-174 The Hard Lefschetz Theorem for Concave and Convex Algebraic Manifolds....Pages 175-187 Sur la résolution des équations de Cauchy-Riemann tangentielles pour les formes à support compact dans les variétés CR ....Pages 188-193 Imbedding pseudohermitian manifolds into a sphere....Pages 194-199 Deformations of Strongly Pseudo-Convex CR Structures and Deformations of Normal Isolated Singularities....Pages 200-204 The Behavior of Multiplier Ideal Sheaves under Morphisms....Pages 205-222 Local Geometry of Decoupled Pseudoconvex Domains....Pages 223-230 A Vanishing Theorem on Kähler Manifolds with Certain Stratified Structures....Pages 231-234 Hodge-Kohomologie und Steinsche Mannigfaltigkeiten....Pages 235-246 The Cauchy-Riemann Equations in Convex Domains....Pages 247-253 Integral Kernels and Hölder Estimates for ∂̄ on Pseudocovnex Domains of Finite Type in C 2 ....Pages 254-257 Complex Analysis in the Golden Fifties....Pages 258-263 On q -Convex Exhaustion Functions of Complements of CR-Submanifolds....Pages 264-267 A Characterization of Homogeneous Bounded Domains....Pages 268-277 Singular Sets of Separately Analytic Functions....Pages 278-286 Some Recent Results Related to the Uniformization Problem in Several Complex Variables....Pages 287-298 Product Decomposition of non reduced Space Germs....Pages 299-305 Modular Subgerms and the Isomorphism Problem in Deformation Theory....Pages 306-309 A new method to introduce a priori estimates for the ∂̄ Neumann problem....Pages 310-314 Maximal and Semi-Maximal Estimates for ∂̄ b on Pseudoconvex Manifolds....Pages 315-323 Degenerations of Instantons....Pages 324-330 Second Main Theorems in Number Theory and Nevanlinna Theory....Pages 331-334 Symplectic Techniques in Holomorphic Group Actions....Pages 335-341 Back Matter....Pages 342-342 Dedicated to H. Grauert on the occasion of his sixtieth birthday, the International Work shop Complex Analysis was held in Wuppertal from February 12 to 16, 1991, with 143 mathematicians participating from all over the world. To the great delight of everybody, an important group of colleagues from the DDR and countries of eastern Europe was able to participate for the first time. The congress was organized by K. Diederich (Wuppertal), J .E. Fornaess (Princeton) and 1. Lieb (Bonn). In complete accordance with the width of the mathematical work of H. Grauert, the congress was intended to give a broad survey over as many areas of active research in complex analysis as possible. Its programm was opened by the lecture "Complex Analysis in the Golden Fifties" by R. Remmert, contained in this volume on page 258. Exposi tory lectures on the history and recent developments of important areas were given by J. Dingener, O. Forster, F. Hirzebruch, J.J. Kohn, L. Lempert, T. Ohsawa, S. 1. Pincuk, O. Riemenschneider and Y.T. Siu. In 82 seminar lectures in 4 parallel groups, recent research was presented to the congress. It was a particular pleasure to see, how many young researchers contributed to this activity 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, Kahler geometry, Lefschetz theorems, holomorphic mappings, Nevanlinna theory, com plex singularities, twistor theory, uniformization.