Several Complex Variables


Fall semester, October 2009 - January 2010

Bo'az Klartag 
Room 229, Schreiber building
Phone: 03-6406957 

Tuesday, 16-18, Kaplun 319 
Wednesday 16-17, Shenkar 13-14

Final grade
There will be 3-5 home assignments throughout the semester. 

Recommended literature All of the following books are available at the library: 

  1. L. Hormander, An introduction to complex analysis in several variables (we will cover chapters 1,2 and 4).
  2. B. Shabat, An introduction to complex analysis, part II (translation from Russian).
  3. S. Krantz, Function theory of several complex variables (more detailed).
  4. R. Narasimhan, Several Complex Variables.
  5. M. Herve, Several Complex Variables.

Functions in several complex variables, pluriharmonic functions, holomorphic and biholomorphic mappings. The phenomenon of forced analytic continuation, Hartogs extension theorem, Reinhardt domains. Domains of holomorphy, d-bar equation. Subharmonic and plurisubharmonic functions, pseudoconvex sets, analogy with real-variable convexity. Existence theorems for d-bar equation, Levi's problem. Prekopa-Leindler and Berdntsson's inequalities, applications to convex geometry. 



The grades of the exercises.