Article ID Journal Published Year Pages File Type
4624071 Journal of Mathematical Analysis and Applications 2006 10 Pages PDF
Abstract

The main result of this paper is the existence of solutions of the equation for closed (0,1)-forms with compact support in a complex fiber bundle from some class. This class of bundles contains, for example, vector bundles. What is important, the solution exists for any base manifold. The solvability property implies many results about extension and representation of complex analytic and Cauchy–Riemann functions: Riemann–Hilbert type representation, Hartogs and Hartogs–Bochner phenomena, vanishing of some cohomology groups, to mention few.

Related Topics
Physical Sciences and Engineering Mathematics Analysis