PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

Title & Authors
PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS
Fridman, Buma L.; Ma, Daowei;

Abstract
The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in $\small{\mathbb{C}^n}$ under small perturbation of this domain in the Hausdorff metric. We consider a number of examples when an arbitrary small perturbation can lead to a domain with a larger group, present theorems concerning upper semicontinuity property of some invariants of automorphism groups. We also prove that the dimension of an abelian subgroup of the automorphism group of a bounded domain in $\small{\mathbb{C}^n}$ does not exceed n.
Keywords
automorphism groups;perturbation of domains;Hausdorff distance;abelian subgroups;
Language
English
Cited by
1.
The automorphism groups of domains in complex space: a survey, Quaestiones Mathematicae, 2013, 36, 2, 225
2.
Model domains in ℂ3with abelian automorphism group, Complex Variables and Elliptic Equations, 2014, 59, 3, 369
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