Complex Analysis and Geometry

When we studied complex variables in the late 1960s, modem geometry on the complex fie1d and complex function theory were identified in teaching and research as several complex variables. A beginner in the field at that time would have the experience of jumping from the sheaf-theoretical methods employed in the theory of analytic spaces to the P.D.E. methods of the ä problem, with the c1ear understanding that the phenomena lying behind such different methods and problems were the same. A few years later, new important discoveries made c1ear that complex differential geometry was also in the same company. Looking at the historical development of the subject in the first half of the twentieth century shows this was not astonishing. The origin of the theory of functions of several complex variables was tardier than the familiar of analytic functions of one complex variable. The first comprehensive theory textbook by Behnke and Thullen, in the 1930s, expounded the foundations ofthe general theory as set up by Weierstrass, Cousin, Hartogs, and Poincare and c1early put in evidence that the difficulties were all but solved. In aseries of papers from 1936 to 1953, Oka introduced a brilliant collection of new ideas and systematically eliminated aU difficulties. Oka's work had in itse1f a fruitful seed and contained the premises for the opening of wider horizons.

Texte du rabat

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Contenu

1. Theory of (a, b)-Modules. I.- 2. On the Fibers of Analytic Mappings.- 3. Twistor Constructions for Vector Bundles.- 4. Monge-Ampère Operators, Lelong Numbers, and Intersection Theory.- 5. CR Analytic Varieties with Given Boundary.- 6. Smooth Pseudoconvex Domains in ?2 for Which the Corona Theorem and Lp Estimates for ?? Fail.- 7. A Characterization of K-Invariant Stein Domains in Symmetric Embeddings.- 8. Complex Structures on the Tangent Bundle of Riemannian Manifolds.- 9. Geometric Realizations of Uniformization of Conjugates of Hermitian Locally Symmetric Manifolds.- 10. Approximation and Extension of Whitney CR Forms.- 11. The Existence of Right Inverses of Residue Homomorphisms.- 12. Tangent Bundles, Rational Curves and the Geometry of Manifolds of Negative Kodaira Dimension.- 13. Boundedness for Nongeneral-Type 3-Folds in ?5.- 14. The Curvature of the Petersson-Weil Metric on the Moduli Space of Kähler-Einstein Manifolds.- 15. On K-Jet Ampleness.- 16. Deformations of Complex Structures on a Real Lie Algebra.- 17. A Problem List on Vector Bundles.- A.1. A List of All Talks Given at the CIRM Conferences on Complex Analysis and Geometry.- A.2. A List of All Participants at the CIRM Conferences on Complex Analysis and Geometry.