TITLE: complex manifold with corner
QUESTION [5 upvotes]: I was reading Dominic Joycee article 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  From here i moved to Melrose unpublished book on Manifold with corner.   
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. 
"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.  
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

REPLY [2 votes]: 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).