• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.563-575
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• 2003

We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to $Aut(C^k {\times}(C^*)^{n - k})$ as topological groups, then M itself is biholomorphically equivalent to C^k{\times}(C^*)^{n - k}$. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.

• East Asian mathematical journal
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• v.31 no.3
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• pp.363-370
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• 2015

The automorphism group of domains is main stream of classification problem coming from E. Cartan's work. In this paper, I introduce classical technique of computations of automorphism group of domains and recent development of automorphism group. Moreover, I suggest new research problems in computations of automorphism group.

• Journal of the Korean Mathematical Society
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• v.40 no.3
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• pp.487-501
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• 2003

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.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.523-561
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• 2008

The purpose of this paper is to survey the use of the important method of scaling in analysis, and particularly in complex analysis. Applications are given to the study of automorophism groups, to canonical kernels, to holomorphic invariants, and to analysis in infinite dimensions. Current research directions are described and future paths indicated.