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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.
List of contents
1: Methods of Partial Differential Equations.- Boundary behavior of holomorphic mappings.- Invariant metrics on pseudoconvex domains.- Local bounds for orders of contact and a conjecture about subellipticity.- On an ideal of ring of differential operators.- Microlocalization of CR structures.- A note on the boundary Laplacian operator.-
2: Methods of Differential Geometry.- Géométrie des compactifications des espaces hermitiens localement symétriques.- Holomorphic projective structures and invariant distances.- Complex-analyticity of harmonic maps and vanishing theorems.- The characterization of strictly parabolic spaces.- The characteristic numbers of 4-dimensional Kähler manifolds.- On the Schwarz lemma for complete hermitian manifolds.- Holomorphic maps and conformal transformation on hermitian manifolds.- The degree of strong nondegeneracy of the bisectional curvature of exceptional bounded symmetric domains.-
3: Holomorphic Vector Bundles.- Holomorphic vector bundles on tori.- Submanifolds of projective space with semi-stable normal bundle.- Parameters for instanton and smoothness of M(0,2).-
4: Kernels and Integral Formulae.- The integral representation for polyhedral domains of ?n.- Removable singularities for holomorphic functions which satisfy the area-BMO condition.- Singular integrals in several complex variables.- Integral formulae in complex analysis.- On the representative domain.- A remark on Poisson kernels.- Some applications of Bochner-Martinelli integral representation.-
5: Pseudoconvexity, Function Fields, Algebraic Varieties, Value Distribution Theory.- Some aspects of pseudoconvexity theory in several complex variables.- A higher dimensional analogue of Mordell's conjecture over function fields and related problems.- Rank-completefunction fields.- Chern classes on algebraic varieties with arbitrary singularities.- A general criterion.- Riemann-Roch theorem for strongly pseudoconvex manifolds of dimension three.
