## Tohoku Mathematical Journal

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

Atsushi Yamamori

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 24 June 2017

https://projecteuclid.org/euclid.tmj/1498269625

Digital Object Identifier
doi:10.2748/tmj/1498269625

Mathematical Reviews number (MathSciNet)
MR3682165

Zentralblatt MATH identifier
06775254

#### Citation

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. https://projecteuclid.org/euclid.tmj/1498269625

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