Math-683(Complex analysis II) (3 hours)  

The main purpose of this course is the study of holomorphic functions in several complex variables.

Introduction : The rigidity properties of holomorphic mappings are one of the most impressive and important features of geometric analysis in several variables . It is well-known that the Riemann mapping theorem does not admits direct reasonable analogues in several variables..

Description

Introduction to holomorphic functions in several variables...General Cauchy’s formula...The  d-bar problem and the  Hartogs theorem, Analytic continuation Pluri-potential theory (Plurisubharmonic functions, invariant metrics...) The Poincare theorem and Fefermann’s theorem. Pseudoconvexity and domain of holomorphy. Automorphism groups( Cartan’s theorem...)

 Text-book

1-      An introduction to Complex analysis in several variables, by Lars Hormander (North-Holland publishing company 1973).

2-       Functions theory of in several complex variables, S. Krantz (John wiley new York, 1982).

3-       Pluripotentiel theory,  M. Klimek (Oxford science publications) 1991.

توزيع الدرجات

Grading

 

 

 

 

 

الاختبار الفصلي الأول

20%

         

20%

1st Midterm

 

 

الاختبار الفصلي الثاني

20%

20%

2nd Midterm

 

الواجبات

10%

10%

Homework

 

الاختبار النهائي

50%

50%

Final Exam

 


 

2-    Exam-2006-2008  :     fexam683.pdf      683Pexam.pdf