Book Review: Lectures on counterexamples in several complex variables

Complex Dynamics in Several Variables

1. Motivation 117 2. Iteration of Maps 118 3. Regular Versus Chaotic Behavior 119 4. The Horseshoe Map and Symbolic Dynamics 120 5. Hénon Maps 123 6. Properties of Horseshoe and Hénon Maps 126 7. Dynamically Defined Measures 127 8. Potential Theory 129 9. Potential Theory in One-Variable Dynamics 131 10. Potential Theory and Dynamics in Two Variables 133 11. Currents and Applications to Dynamic...

Lecture notes on several complex variables

A Priori Estimates in Several Complex Variables

Classically there are two points of view in the study of global existence problems in the theory of functions of a complex variable. One is to piece together local solutions (such as power series), always staying within the category of holomorphic functions. This method seems to have been initiated by Weierstrass; in the theory of several complex variables it has been implemented by the study o...

On Identical Vanishing of Holomorphic Functions in Several Complex Variables.

We will make some comment on the following recent result of J. J. Kohn. In the complex space Cn:(z1, . . . , zn) if fl, . . . , fn are holomorphic in the unit ball and have continuous boundary values on the boundary, and if on the boundary the linear combination 1fi+ + j,,f is 0, then the functions fl, . .. , f,, are identically 0. 1. We denote by D any bounded circular domain in C., by B its b...

On Some Problems in Several Complex Variables and Cr Geometry

0. Introduction. Geometric analysis in several complex variables and Cauchy Riemann geometry has been a quite active subject in pure and applied mathematics for decades. The classical work of Poincaré, Hartogs, Levi, E. Cartan, etc at the beginning of the century laid down part of the frame work of such a study. Since then, more and more attention has be paid to this field, as people discover i...