Approximation and Extension of Whitney CR Forms

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

Abstract

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.

Keywords

Exact Sequence Holomorphic Function Closed Subset Complex Manifold Ambient Space 
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 1993

Authors and Affiliations

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

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