Several Complex Variables is a central area of mathematics with strong interactions with partial differential equations, algebraic geometry, number theory, and differential geometry. The 1995-1996 MSRI program on Several Complex Variables emphasized these interactions and concentrated on developments and problems of interest that capitalize on this interplay of ideas and techniques. This collection, first published in 2000, provides a remarkably clear and complete picture of the status of research in these overlapping areas and will provide a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students to the use of techniques from these other areas in several complex variables. Thanks to its distinguished list of contributors this volume provides a representative sample of the work done in Several Complex Variables.

The contributions in this major work focus on a central area of mathematics with strong ties to partial differential equations, algebraic geometry, number theory, and differential geometry. The 1995-96 MSRI program on Several Complex Variables emphasized these interactions and concentrated on current developments and problems that capitalize on this interplay of ideas and techniques. This collection provides a remarkably complete picture of the status of research in these overlapping areas and a basis for significant continued contributions from researchers. Several of the articles are expository or have extensive expository sections, making this an excellent introduction for students on the use of techniques from these other areas in several complex variables. This volume comprises a representative sample of some of the best work recently done in Several Complex Variables.

The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field.

The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.