대한수학회지 (Journal of the Korean Mathematical Society)

  • 제40권3호
  • /
  • Pages.487-501
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  • 2003
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 발행 : 2003.05.06
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초록

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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참고문헌

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피인용 문헌

  1. The automorphism groups of domains in complex space: a survey vol.36, pp.2, 2013, https://doi.org/10.2989/16073606.2013.779982
  2. Model domains in ℂ3with abelian automorphism group vol.59, pp.3, 2014, https://doi.org/10.1080/17476933.2012.734505