The Scaling Method, I

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


If a bounded domain \(\Omega\) in \(\mathbb{C}{^n}\) has a noncompact automorphism group, then all the orbits of the automorphism group are noncompact (Proposition 1.3.10). Thus each orbit must “go out to the boundary” of the domain \(\Omega\), since orbits are closed in \(\Omega\) (Corollary 1.3.6).


Compact Subset Holomorphic Mapping Boundary Point Open Neighborhood Open Unit Disc 
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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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