Geometry Seminar

 

Proper holomorphic maps of Reinhardt domains

 

Professor Alexander Isaev

Australian National University, Canberra

 

Abstract

Proper holomorphic maps are natural generalizations of biholomorphic maps and often arise in problems of complex analysis and geometry. In this talk I will concentrate on proper holomorphic maps between  Reinhardt domains in complex space (a domain is called Reinhardt if it is invariant under rotations in each variable). One motivation for this study is a classical theorem due to H. Alexander (1977) that states that every proper holomorphic self-map of a ball in complex space is in fact biholomorphic. There have been many generalizations of this result, but the question of describing all Reinhardt domains for which every proper holomorphic self-map is a holomorphic automorphism has been open until recently even in dimension 2. In my talk I present a complete solution to this problem. It is a corollary of a more general result, which is a complete description of all proper holomorphic maps between Reinhardt domains in dimension 2. This work is joint with N. Kruzhilin (Steklov Mathematical Institute, Moscow).

 

Date:

March 29, 2007 (Thursday)

Time:

3:00 – 4:00pm

Place:

Room 517, Meng Wah Complex, HKU

 

 

All are welcome