Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

  • Fridman, Buma L. (Department of Mathematics Wichita State University) ;
  • Ma, Daowei (Department of Mathematics Wichita State University)
  • Published : 2003.05.06
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Abstract

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

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