∂̅-cohomology and geometry of the boundary of pseudoconvex domains

• Autorzy: Takeo Ohsawa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32V40: Real submanifolds in complex manifolds
• 53C40: Global submanifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2007
• Tom: 91
• Numer: 2-3
• Strony: 249-262

Daty

wydano

2007

Twórcy

autor

Takeo Ohsawa

• Graduate School of Mathematics, Nagoya University, Chikusaku Furocho, 464-8602 Nagoya, Japan

Identyfikatory

DOI

10.4064/ap91-2-12