Complex Analysis and Geometry

ISBN-13: 9781475797732 / Angielski / Miękka / 2013 / 412 str.

Vincenzo Ancona; Alessandro Silva

Opis

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 a- 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.

Spis treści

Theory of (A,B)Modules; D. Barlet. On the Fibers of Analytic Mappings; J. Bingener, H. Flenner. Twister Constructions for Vector Bundles; P. de Bartolomeis. Monge-Ampére Operators, Lelong Numbers, and Intersection Theory; J.P. Demailly. CR Analytic Varieties with Given Boundary; P. Dolbeault. A Characterization of KInvariant Stein Domains in Symmetric Embeddings; A.T. Huckleberry, G. Fels. Complex Structures on the Tangent Bundle of Riemannian Manifolds; L. Lempert. Geometric Realizations of Uniformization of Conjugates of Hermitian Locally Symmetric Manifolds; N. Mok, S.K. Yeung. Approximation and Extension of Whitney CR Forms; M. Nacinovich. Tangent Bundles, Rational Curves, and the Geometry of Manifolds of Negative Kodaira Dimension; T. Peternell. A Problem List on Vector Bundles; E. Ballico. 8 additional articles. Index.