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manuscripta mathematica

, Volume 112, Issue 4, pp 403–431 | Cite as

Lineally convex domains of finite type: holomorphic support functions

  • Klas DiederichEmail author
  • John Erik Fornæss
Article

Abstract.

Smooth bounded lineally convex domains of finite type constitute a natural class of domains in complex analysis, since they are locally biholomorphically invariant. A smooth family of holomorphic support functions is constructed by an almost explicit formula on every such domain. It satisfies the best possible estimates near the point of support on every two-dimensional transverse affine intersection with the domain. Together with a suitable pseudometric on these domains, it will allow to do precise quantitative complex analysis by integral kernels on them.

Keywords

Explicit Formula Complex Analysis Support Function Convex Domain Finite Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.MathematikUniversität WuppertalWuppertalGermany
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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