Perturbation of domains and automorphism groups

Details Perturbation of domains and automorphism groups Perturbation of domains and automorphism groups

2002-11-30

arxiv.org/abs/math/0212005v1

Mathematics

Complex Variables

14 pages

Scientific paper

The paper is devoted to the description of changes of the structure of the holomorphic automorphism group of a bounded domain in ${\Bbb C}^n$ 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 ${\Bbb C}^n$ does not exceed $n$.

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