Approximation and Extension of Whitney CR Forms
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  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.
KeywordsExact Sequence Holomorphic Function Closed Subset Complex Manifold Ambient Space
Unable to display preview. Download preview PDF.
- 14.M. Nacinovich, On a theorem of Airapetyan and Henkin, preprint, Dip. Mat. Pisa No. 431 (1989).Google Scholar