Title

Holomorphic Extensions in Complex Fiber Bundles

Abstract

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

complex manifolds; cr functions; fiber bundles

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Elsevier, All rights reserved.


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