| Title:
|
Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains (English) |
| Author:
|
Guo, Ting |
| Author:
|
Feng, Zhiming |
| Author:
|
Bi, Enchao |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
71 |
| Issue:
|
2 |
| Year:
|
2021 |
| Pages:
|
373-386 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 ${\rm e}^{\mu \|z\|^{2}}\sum _{j=1}^{m}|\omega _{j}|^{2p}<1$, where $(z,\omega )\in \mathbb {C}^n\times \mathbb {C}^m$. 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 $\sum _{j=1}^{m}|\omega _{j}|^{2p}{\rm e}^{\mu \|z\|^{2}}$ invariant. (English) |
| Keyword:
|
generalized Fock-Bargmann-Hartogs domain |
| Keyword:
|
holomorphic automorphism group |
| MSC:
|
32H35 |
| idZBL:
|
07361074 |
| idMR:
|
MR4263175 |
| DOI:
|
10.21136/CMJ.2020.0364-19 |
| . |
| Date available:
|
2021-05-20T13:41:03Z |
| Last updated:
|
2023-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148910 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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