complex manifold with corner - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T06:20:52Z http://mathoverflow.net/feeds/question/96318 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96318/complex-manifold-with-corner complex manifold with corner Jonujohn 2012-05-08T09:44:45Z 2012-05-18T06:53:10Z <p>I was reading Dominic Joycee <a href="http://arxiv.org/abs/0910.3518" rel="nofollow">article</a> on Manifold with corner. He talk about manifold with corner modeled over $[0,\infty)^k\times \mathbb R^{n-k}$ for some $k\leq n$. From here i moved to Melrose unpublished book on Manifold with corner. </p> <p>Is the theory for Complex manifold with boundary and corner is developed. I mean is there some literature available where complex manifold with corner has been discussed. </p> <p>"Complex manifold with corner" is a vague word. But i mean, i want to see as $[0,1]\times [0,1]$ as complex manifold with corner where boundary is CR manifold. </p> <p>I think "main problem" is the extension of holomorphic function defined in the interior of domain. In real case, we have whitney extension theorem.... There may be many other issues... Can i have reference, suggested reading along these lines. Thanks </p> http://mathoverflow.net/questions/96318/complex-manifold-with-corner/96321#96321 Answer by Daniele Zuddas for complex manifold with corner Daniele Zuddas 2012-05-08T10:34:54Z 2012-05-08T10:34:54Z <p>There are some related results about compact Stein 4-manifolds with boundary as Lefschetz fibrations over the disk (whose fiber has non-empty boundary). Corners in this case arise naturally on the total space. References includes Loi-Piergallini's theorem, and subequent works of Akbulut-Ozbagci (simply google with these keywords).</p>