• Robert E. Greene
  • Kang-Tae Kim
  • Steven G. Krantz
Part of the Progress in Mathematics book series (PM, volume 291)


A subset \(\Omega \subseteq \mathbb{C}{^n}\) will be called a domain if it is connected and open. The automorphism group Aut \((\Omega)\) of \(\Omega\) is by definition the set of all holomorphic mappings \(f:\Omega \to \Omega\) with inverse map \({f^{ - 1}}\) existing and also holomorphic. The group operation is the composition of mappings, and it is easy to check that this binary operation makes Aut \((\Omega)\) into a group.


Riemann Surface Compact Subset Holomorphic Function Automorphism Group Complex Manifold 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Robert E. Greene
    • 1
  • Kang-Tae Kim
    • 2
  • Steven G. Krantz
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsPohang Institute of Science and TechnologyPohangSouth Korea
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA

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