Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains

Guo, Ting, Feng, Zhiming, and Bi, Enchao. "Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains." Czechoslovak Mathematical Journal 71.2 (2021): 373-386. <http://eudml.org/doc/298013>.

@article{Guo2021,
abstract = {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 $\{\rm e\}^\{\mu \Vert z\Vert ^\{2\}\}\sum _\{j=1\}^\{m\}|\omega _\{j\}|^\{2p\}<1$, 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 $\sum _\{j=1\}^\{m\}|\omega _\{j\}|^\{2p\}\{\rm e\}^\{\mu \Vert z\Vert ^\{2\}\}$ invariant.},
author = {Guo, Ting, Feng, Zhiming, Bi, Enchao},
journal = {Czechoslovak Mathematical Journal},
keywords = {generalized Fock-Bargmann-Hartogs domain; holomorphic automorphism group},
language = {eng},
number = {2},
pages = {373-386},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains},
url = {http://eudml.org/doc/298013},
volume = {71},
year = {2021},
}

TY - JOUR
AU - Guo, Ting
AU - Feng, Zhiming
AU - Bi, Enchao
TI - Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains
JO - Czechoslovak Mathematical Journal
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 71
IS - 2
SP - 373
EP - 386
AB - 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 ${\rm e}^{\mu \Vert z\Vert ^{2}}\sum _{j=1}^{m}|\omega _{j}|^{2p}<1$, 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 $\sum _{j=1}^{m}|\omega _{j}|^{2p}{\rm e}^{\mu \Vert z\Vert ^{2}}$ invariant.
LA - eng
KW - generalized Fock-Bargmann-Hartogs domain; holomorphic automorphism group
UR - http://eudml.org/doc/298013
ER -