arXiv math/04125042004-12math.CVmath.AP

Analytic discs, plurisubharmonic hulls, and non-compactness of the d-bar-Neumann operator

Sonmez Sahutoglu, Emil J. Straube

备注：: 10 pages
发表信息：: Math. Ann. 334 (2006), no. 4, 809--820
DOI：: 10.1007/s00208-005-0737-0

英文摘要：

We show that a complex manifold M in the boundary of a smooth bounded pseudoconvex domain in C^n is an obstruction to compactness of the d-bar-Neumann operator on the domain, provided that at some point of M, the Levi form has the maximal possible rank n-1-dim(M) (i.e. the domain is strictly pseudoconvex in the directions transverse to M). In particular, an analytic disc is an obstruction, provided that at some point of the disc, the Levi form has only one zero eigenvalue. We also show that a boundary point where the Levi form has only one zero eigenvalue can be picked up by the plurisubharmonic hull of a set only via an analytic disc in the boundary.

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