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Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan’s linearity theorem and explicit Bergman kernel. (English) Zbl 1388.32014
In several complex variables, complex domains which are bounded or hyperbolic are fundamental research objects. For unbounded non-hyperbolic cases, only few results are known about the structure of the holomorphic automorphism groups. The main result of the paper under review gives a class of unbounded non-hyperbolic Reinhardt domains with non-compact automorphism groups, Cartan’s linearity theorem, and explicit Bergman kernels. Moreover, a reformulation of Cartan’s linearity theorem for finite volume Reinhardt domains is given.
Reviewer: Rong Du (Shanghai)
##### MSC:
 32M05 Complex Lie groups, group actions on complex spaces 32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.) 32A07 Special domains in $${\mathbb C}^n$$ (Reinhardt, Hartogs, circular, tube) (MSC2010)
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