NON-HYPERBOLIC UNBOUNDED REINHARDT DOMAINS: NON-COMPACT AUTOMORPHISM GROUP, CARTAN'S LINEARITY THEOREM AND EXPLICIT BERGMAN KERNEL

摘要

In the study of the holomorphic automorphism groups, many researches have been carried out inside the category of bounded or hyperbolic domains. On the contrary to these cases, for unbounded non-hyperbolic cases, only a few results are known about the structure of the holomorphic automorphism groups. Main result of the present paper gives a class of unbounded non-hyperbolic Reinhardt domains with non-compact automorphism groups, Car tan's linearity theorem and explicit Bergman kernels. Moreover, a reformulation of Caftan's linearity theorem for finite volume Reinhardt domains is also given.