A Coda on Domains of Finite Type

  • Steven G. Krantz
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

The idea of finite type was first developed by J.J. Kohn in the study of subelliptic estimates for the \(\overline{\partial}\)-Neumann problem (see [KOH1]). It has grown and evolved into a fundamental idea in geometric function theory. It is an important geometric invariant, one that we can calculate. Properly viewed, it is the right generalization of strong pseudoconvexity. The book [DAN5] gives a comprehensive survey of the theory. The idea of finite type is fundamental both to the partial differential equations of several complex variables and also to a variety of mapping problems. It is considerably more complex in the n-variable setting than in the 2-variable setting.


Holomorphic Function Neumann Problem Finite Type Pseudoconvex Domain Levi Form 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dept. MathematicsWashington UniversitySt.LouisUSA

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