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International Journal of Mathematics and Mathematical Sciences
Volume 2014 (2014), Article ID 160579, 5 pages
http://dx.doi.org/10.1155/2014/160579
Research Article

A New Proof for the Description of Holomorphic Flows on Multiply Connected Domains

1Department of Mathematics, University of Wyoming, Laramie, WY 82071, USA
2Department of Mathematics, Statistics and Computer Science, University of Illinois, Chicago, IL 60612, USA
3Department of Mathematical Sciences, University of Montana, Missoula, MT 59812, USA

Received 14 October 2013; Accepted 6 February 2014; Published 13 March 2014

Academic Editor: S. M. Gusein-Zade

Copyright © 2014 F. Jafari et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We provide a new proof for the description of holomorphic and biholomorphic flows on multiply connected domains in the complex plane. In contrast to the original proof of Heins (1941) we do this by the means of operator theory and by utilizing the techniques of universal coverings of the underlying domains of holomorphic flows and their liftings on the corresponding universal coverings.