Tohoku Mathematical Journal

Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel

Atsushi Yamamori

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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.

Article information

Tohoku Math. J. (2), Volume 69, Number 2 (2017), 239-260.

First available in Project Euclid: 24 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32M05: Complex Lie groups, automorphism groups acting on complex spaces [See also 22E10]
Secondary: 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)

Bergman kernel holomorphic automorphism group Reinhardt domain


Yamamori, Atsushi. Non-hyperbolic unbounded Reinhardt domains: non-compact automorphism group, Cartan's linearity theorem and explicit Bergman kernel. Tohoku Math. J. (2) 69 (2017), no. 2, 239--260. doi:10.2748/tmj/1498269625.

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