Holomorphic Extensions in Complex Fiber Bundles
The main result of this paper is the existence of solutions of the equation View the MathML source 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.
R. Dwilewicz, "Holomorphic Extensions in Complex Fiber Bundles," Journal of Mathematical Analysis and Applications, Elsevier, Jan 2006.
The definitive version is available at https://doi.org/10.1016/j.jmaa.2005.09.044
Mathematics and Statistics
Keywords and Phrases
complex manifolds; cr functions; fiber bundles
International Standard Serial Number (ISSN)
Article - Journal
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