Holomorphic Extension of CR Functions: A Survey

  • Jean-Marie Trépreau
Conference paper
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 21)


A CR function on a generic real submanifold of Cn is a solution of the induced Cauchy-Riemann system; for example, traces of holomorphic functions are CR. This lecture will be a survey, intended for the non-specialist, of the results obtained during the last ten years on the question of the holomorphic extendibility of CR functions. Emphasis will be put on the method of the complex disc, the Bishop equation, and Tumanov’s theorem on the holomorphic extendibility into a wedge from minimal manifolds. The basic notions about CR functions will be introduced and several important results will be presented.


Holomorphic Function Finite Type Extension Property Real Hypersurface Holomorphic Extension 
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 Science+Business Media New York 1996

Authors and Affiliations

  • Jean-Marie Trépreau
    • 1
  1. 1.Institut de MathématiquesUniversité de Paris VIParis Cedex 05France

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