Approximation and Extension of Whitney CR Forms

  • Mauro Nacinovich
Part of the The University Series in Mathematics book series (USMA)


In this Chapter I want to outline some results on the approximation and extension of functions and forms that are defined in the sense of Whitney on closed subsets of a complex manifold and that satisfy the Cauchy-Riemann equations. Attention to such objects was first drawn by the study of the tangential Cauchy-Riemann complex, as in Andreotti and Hill [3] by the use of a Mayer-Vietoris sequence relating the cohomology of this complex to that of the ambient space. However, the Whitney cohomology appears as a natural object to be considered in more general situations and provides a unique framework to understand different situations, encompassing the classical Oka extension theorem and the question of approximating functions defined on a totally real subset by holomorphic functions in the ambient space. The results are obtained for zero sets of ideals of holomorphic functions that satisfy the conditions of Lojasiewicz, and I think it would be interesting to pursue the question of the general characterization of the object that I introduce here.


Exact Sequence Holomorphic Function Closed Subset Complex Manifold Ambient Space 
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Copyright information

© Springer Science+Business Media New York 1993

Authors and Affiliations

  • Mauro Nacinovich
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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