Tohoku Mathematical Journal
2017
June
SECOND SERIES VOL. 69, NO. 2

Tohoku Math. J.
69 (2017), 239-260

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

Author Atsushi Yamamori

(Received May 18, 2015, revised August 3, 2015)
Abstract. 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, Cartan's linearity theorem and explicit Bergman kernels. Moreover, a reformulation of Cartan's linearity theorem for finite volume Reinhardt domains is also given.

Mathematics Subject Classification. Primary 32M05; Secondary 32A25.
Key words and phrases. Bergman kernel, holomorphic automorphism group, Reinhardt domain.

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