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The geometry of real submanifolds in complex manifolds and the
analysis of their mappings belong to the most advanced streams of
contemporary Mathematics. In this area converge the techniques of
various and sophisticated mathematical fields such as P.D.E.s,
boundary value problems, induced equations, analytic discs in
symplectic spaces, complex dynamics. For the variety of themes and
the surprisingly good interplaying of different research tools,
these problems attracted the attention of some among the best
mathematicians of these latest two decades. They also entered as a
refined content of an advanced education. In this sense the five
lectures of this volume provide an excellent cultural background
while giving very deep insights of current research activity.
The papers in this volume cover many important topics of current
interest in partial differential equations and several complex
variables. An international group of well-known mathematicians has
contributed original research articles on diverse topics such as
the geometry of complex manifolds, the mean curvature equation,
formal solutions of singular partial differential equations, and
complex vector fields. The material in this volume is useful for
graduate students and researchers interested in partial
differential equations and several complex variables.
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