Ebook: Several Complex Variables: Proceedings of the 1981 Hangzhou Conference

In recent years there has been increasing interaction among various branches of mathematics. This is especially evident in the theory of several complex variables where fruitful interplays of the methods of algebraic geometry, differential geometry, and partial differential equations have led to unexpected insights and new directions of research. In China there has been a long tradition of study in complex analysis, differential geometry and differential equations as interrelated subjects due to the influence of Professors S. S. Chern and L. K. Hua. After a long period of isolation, in recent years there is a resurgence of scientific activity and a resumption of scientific exchange with other countries. The Hangzhou conference is the first international conference in several complex variables held in China. It offered a good opportunity for mathematicians from China, U.S., Germany, Japan, Canada, and France to meet and to discuss their work. The papers presented in the conference encompass all major aspects of several complex variables, in particular, in such areas as complex differential geometry, integral representation, boundary behavior of holomorphic functions, invariant metrics, holomorphic vector bundles, and pseudoconvexity. Most of the participants wrote up their talks for these proceedings. Some of the papers are surveys and the others present original results. This volume constitutes an overview of the current trends of research in several complex variables.

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Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Boundary Behavior of Holomorphic Mappings....Pages 3-6
Invariant metrics on pseudoconvex domains....Pages 7-12
Local Bounds for Orders of Contact and a Conjecture about Subellipticity....Pages 13-18
On an Ideal of Ring of Differential Operators....Pages 19-28
Microlocalization of CR structures....Pages 29-36
A Note on the Boundary Laplacian Operator....Pages 37-54
Front Matter....Pages 55-55
Geometrie Des Compactifications Des Espaces Hermitiens Localement Symetriques....Pages 57-66
Holomorphic Projective Structures and Invariant Distances....Pages 67-71
Complex-Analyticity of Harmonic Maps and Vanishing Theorems....Pages 73-84
The Characterization of Strictly Parabolic Spaces....Pages 85-94
The Characteristic Numbers of 4-Dimensional K?hler Manifolds....Pages 95-97
On the Schwarz Lemma for Complete Hermitian Manifolds....Pages 99-116
Holomorphic Maps and Conformal Transformation on Hermitian Manifolds....Pages 117-126
The degree of strong nondegeneracy of the bisectional curvature of exceptional bounded symmetric domains....Pages 127-139
Front Matter....Pages 141-141
Holomorphic vector bundles on tori....Pages 143-149
Submanifolds of Projective Space with Semi-Stable Normal Bundle....Pages 151-160
Parameters for Instanton Bundles and Smoothness of M(0,2)....Pages 161-166
Front Matter....Pages 167-167
Removable Singularities for Holomorphic Functions which Satisfy the Area-BMO Condition....Pages 169-173
Singular Integrals in Several Complex Variables....Pages 175-180
Front Matter....Pages 181-185
Integral Formulae in Complex Analysis....Pages 167-167
On the Representative Domain....Pages 187-197
A Remark on Poisson Kernels....Pages 199-211
Some Applications of Bochner-Martinelli Integral Representation....Pages 213-216
Front Matter....Pages 217-225
Some Aspects of Pseudoconvexity Theory in Several Complex Variables....Pages 227-227
A Higher Dimensional Analogue of Mordell’s Conjecture Over Function Fields and Related Problems....Pages 229-235
Rank-complete function fields....Pages 237-244
Chern classes on algebraic varieties with arbitrary singularities....Pages 245-246
A General Criterion....Pages 247-249
Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension Three....Pages 251-255
....Pages 257-267