This volume comprises the proceedings of a conference on the geometric analysis of several complex variables held at POSTECH in June 1997. The conference was attended by scientists and students from around the globe.

Each of the five plenary speakers at the conference gave a short course on a topic of current interest in the field. The lecture write-ups contain cogent and accessible information intended for a broad audience. The volume also includes a tutorial in several complex variables given by Kim and Krantz at the conference. This tutorial is geared toward helping the novice to understand the rest of the material in the book.

The bibliographies of the papers give students and young mathematicians a valuable resource for future learning on the topic. This book provides a substantial overview on areas of current activity. Required background for understanding the text is a solid undergraduate education in mathematics and familiarity with first-year graduate studies in real and complex analysis. Some exposure to geometry would be helpful. The book is also suitable for use as a supplemental course text.

Readership

Graduate students, educators, experienced and novice research mathematicians interested in real and complex analysis.

Table of Contents

• K.-T. Kim and S. G. Krantz -- A crash course in the function theory of several complex variables

• E. Bedford and J. Smillie -- External rays in the dynamics of polynomial automorphisms of \({\mathbf C}^2\)
• N. Mok -- \(G\)-structures on irreducible Hermitian symmetric spaces of rank \(\geq 2\) and deformation rigidity
• J. Noguchi -- Value distribution theory of holomorphic mappings
• J.-P. Rosay -- Automorphisms of \(\mathbb{C}^n\), a survey of Andersén-Lempert theory and applications

• M. Abate and G. Patrizio -- Convex-like properties of the Teichmüller metric
• M. Abate and R. Tauraso -- The Julia-Wolff-Carathéodory theorem(s)
• U. Backlund and A. Fällström -- Maximal ideals in \(A(\Omega)\)
• Z. Błocki -- On the regularity of the complex Monge-Ampère operator
• H. R. Cho -- \(L^p\) and \(H^p\) extensions of holomorphic functions from subvarieties
• H. Derksen and F. Kutzschebauch -- Global holomorphic linearization of actions of compact Lie groups on \(\mathbb{C}^n\)
• P. M. Gauthier -- Covering properties of holomorphic mappings
• A. Hayashimoto -- On the relations between the holomorphic extendability theorems and the finiteness properties
• K.-T. Kim and A. F. Spiro -- Moduli space of ramified holomorphic coverings of \(B^2\)
• S. Kołodziej -- A sufficient condition for solvability of the Dirichlet problem for the complex Monge-Ampère operator
• M. Landucci -- \(\Gamma\)-invariant polynomials and proper maps
• J.-P. Rosay -- A simple proof of uniqueness for perturbations of the Mizohata operator