• 제목/요약/키워드: holomorphic automorphism groups

검색결과 4건 처리시간 0.023초

A CHARACTERIZATION OF Ck×(C*) FROM THE VIEWPOINT OF BIHOLOMORPHIC AUTOMORPHISM GROUPS

  • Kodama, Akio;Shimizu, Satoru
    • 대한수학회지
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    • 제40권3호
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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.

NEW AND OLD RESULTS OF COMPUTATIONS OF AUTOMORPHISM GROUP OF DOMAINS IN THE COMPLEX SPACE

  • Byun, Jisoo
    • East Asian mathematical journal
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    • 제31권3호
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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.

PERTURBATION OF DOMAINS AND AUTOMORPHISM GROUPS

  • Fridman, Buma L.;Ma, Daowei
    • 대한수학회지
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    • 제40권3호
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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.

COMPLEX SCALING AND GEOMETRIC ANALYSIS OF SEVERAL VARIABLES

  • Kim, Kang-Tae;Krantz, Steven G.
    • 대한수학회보
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    • 제45권3호
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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.