Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

∂̅-cohomology and geometry of the boundary of pseudoconvex domains

100%

Ohsawa T.

Annales Polonici Mathematici

2007

tom 91

nr 2-3

249-262

In 1958, H. Grauert proved: If D is a strongly pseudoconvex domain in a complex manifold, then D is holomorphically convex. In contrast, various cases occur if the Levi form of the boundary of D is everywhere zero, i.e. if ∂D is Levi flat. A review is given of the results on the domains with Levi flat boundaries in recent decades. Related results on the domains with divisorial boundaries and generically strongly pseudoconvex domains are also presented. As for the methods, it is explained how Hartogs type extension theorems and L² finiteness theorem for the Ī-cohomology are applied.

Hartogs type extension theorems on some domains in Kähler manifolds

100%

Ohsawa T.

Annales Polonici Mathematici

2012

tom 106

nr 1

243-254

Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and ∂Ω is the support of a divisor whose normal bundle is nonflatly semipositive.

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Ohsawa T.

1 2012

1 2007

Wyniki wyszukiwania

∂̅-cohomology and geometry of the boundary of pseudoconvex domains

Hartogs type extension theorems on some domains in Kähler manifolds