On a minimum principle in several complex variables

On the minimum of several random variables

For a given sequence of real numbers a1, . . . , an we denote the k-th smallest one by k-min1≤i≤n ai. Let A be a class of random variables satisfying certain distribution conditions (the class contains N(0, 1) Gaussian random variables). We show that there exist two absolute positive constants c and C such that for every sequence of positive real numbers x1, . . . , xn and every k ≤ n one has c...

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...

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...

Lecture notes on several complex variables

A short introduction to several complex variables

This text is a short two hour introduction into the theory of several complex variables. These lectures were given in May 1996 at Caltech to the class Ma 108 substituting for someone else. As prerequisite, the topic requires some familiarity with complex analysis in one dimension. The higher dimensional generalization of complex analysis in one variables is an important part of mathematics. Our...