Cousin Domains in a Kähler Surface With Positive Holomorphic Bisectional Curvature

Complex surfaces with vanishing cohomology and projective closures

“…is a Ka¨hler metric on M and : D À! ð0, 1Þ the corresponding boundary distance function, then by [20] there exists a constant c 2 R such that the Levi form of À log (computed in the distributional sense) is bounded from below by c!. The idea was to look at the function :¼ Àlog þ M' with M > 0; for M large enough becomes strictly plurisubharmonic on D. But, and here is the gap, it is not clear why remains exhaustive (since ' may tend to À1 at some boundary point of D).…”

“…Motivated by this kind of result in a series of papers ( [18][19][20][21] In this article we shall reconsider the aforeseen problem in a more general setting; our main result is Theorem 1. Before stating it, let us recall a bit of terminology.…”