most recent 30 from http://mathoverflow.net 2013-05-20T01:21:40Z http://mathoverflow.net/feeds/question/94503 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/94503/domain-of-holomorphy Maria Conceição 2012-04-19T07:17:16Z 2012-04-19T07:17:16Z

<p>How to show that $D={ |z_1|&lt;1} \cup { |z_2|&lt;1} \subset \mathbb{C}^2$ is not a domain of holomorphy. What is the smallest domain of holomorphy $ S\supset D $ ?</p> <p>I think we cannot just add the distinguished boundary (the torus $|z_1|=1, |z_2|=1$) to $D$ because it would violate analiticity. Should we use logarithmically convexity argument to extend our domain? Can anyone help?</p> <p>Thank you!</p>