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This volume consists of a collection of articles for the
proceedings of the 40th Taniguchi Symposium Analysis and Geometry
in Several Complex Variables held in Katata, Japan, on June 23-28,
1997. Since the inhomogeneous Cauchy-Riemann equation was
introduced in the study of Complex Analysis of Several Variables,
there has been strong interaction between Complex Analysis and Real
Analysis, in particular, the theory of Partial Differential
Equations. Problems in Complex Anal ysis stimulate the development
of the PDE theory which subsequently can be applied to Complex
Analysis. This interaction involves Differen tial Geometry, for
instance, via the CR structure modeled on the induced structure on
the boundary of a complex manifold. Such structures are naturally
related to the PDE theory. Differential Geometric formalisms are
efficiently used in settling problems in Complex Analysis and the
results enrich the theory of Differential Geometry. This volume
focuses on the most recent developments in this inter action,
including links with other fields such as Algebraic Geometry and
Theoretical Physics. Written by participants in the Symposium, this
vol ume treats various aspects of CR geometry and the Bergman
kernel/ pro jection, together with other major subjects in modern
Complex Analysis. We hope that this volume will serve as a resource
for all who are interested in the new trends in this area. We would
like to express our gratitude to the Taniguchi Foundation for
generous financial support and hospitality. We would also like to
thank Professor Kiyosi Ito who coordinated the organization of the
symposium."
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