Holomorphic Extensions in Complex Fiber Bundles

Author

Roman Dwilewicz, Missouri University of Science and TechnologyFollow

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.

Recommended Citation

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

Department(s)

Mathematics and Statistics

Keywords and Phrases

complex manifolds; cr functions; fiber bundles

International Standard Serial Number (ISSN)

0022-247X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2006 Elsevier, All rights reserved.

Publication Date

01 Jan 2006