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Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains
Czechoslovak Mathematical Journal ( IF 0.5 ) Pub Date : 2020-04-17 , DOI: 10.21136/cmj.2020.0364-19
Ting Guo , Zhiming Feng , Enchao Bi

We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain $$D_{n,m}^p(\mu )$$ . The generalized Fock-Bargmann-Hartogs domain is defined by inequality $${e^{\mu {{\left\| z \right\|}^2}}}\sum\limits_{j = 1}^m {{{\left| {{\omega _j}} \right|}^{2p}} < 1} $$ , where $$\left( {z,\omega } \right) \in {\mathbb{C}^n} \times {\mathbb{C}^m}$$ . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain $$D_{n,m}^p(\mu )$$ becomes a holomorphic automorphism if and only if it keeps the function $$\sum\limits_{j = 1}^m {{{\left| {{\omega _j}} \right|}^{2p}}{e^{\mu {{\left\| z \right\|}^2}}}} $$ invariant.

中文翻译:

广义 Fock-Bargmann-Hartogs 域的全纯自同构的刚性

我们研究一类典型的 Hartogs 域,称为广义 Fock-Bargmann-Hartogs 域 $$D_{n,m}^p(\mu )$$ 。广义 Fock-Bargmann-Hartogs 域由不等式 $${e^{\mu {{\left\| z \right\|}^2}}}\sum\limits_{j = 1}^m {{{\left| {{\omega _j}} \right|}^{2p}} < 1} $$ ,其中 $$\left( {z,\omega } \right) \in {\mathbb{C}^n} \times {\mathbb{C}^m}$$ 。在本文中,我们将建立其全纯自同构群的刚性。我们的结果意味着广义 Fock-Bargmann-Hartogs 域 $$D_{n,m}^p(\mu)$$ 的全纯自映射成为全纯自同构当且仅当它保持函数 $$\sum \limits_{j = 1}^m {{{\left| {{\omega _j}} \right|}^{2p}}{e^{\mu {{\left\| z \right\|}^2}}}} $$ 不变。
更新日期:2020-04-17
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