The Scaling Method, II

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


In the preceding chapter, we discussed theorems concerning the characterization of bounded domains in \(\mathbb{C}{^n}\) by their boundary geometry and the noncompactness of their automorphism groups. There, the scaling method served as a medium that produces the “best” holomorphic re-embedding of the domain into \(\mathbb{C}{^n}\). Thus the scaling method replaced the role of the study of asymptotic boundary behavior of holomorphic invariants.


Open Neighborhood Pseudoconvex Domain Bergman Kernel Holomorphic Sectional Curvature Bergman Kernel Function 
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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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