International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 10, Pages 621-625

The union problem on complex manifolds

Patrick W. Darko

Department of Mathematics and Computer Science, Lincoln University, Lincoln University 19352, PA, USA

Received 14 May 2001

Copyright © 2002 Patrick W. Darko. 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.


Let Ω be a relatively compact subdomain of a complex manifold, exhaustable by Stein open sets. We give a necessary and sufficient condition for Ω to be Stein, in terms of L2 -estimates for the ¯-operator, equivalent to the condition of Markoe (1977) and Silva (1978).