Proper
holomorphic maps of Reinhardt domains
Professor Alexander Isaev
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,
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Room 517, Meng Wah Complex, HKU |
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All are
welcome |
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