∂̅-cohomology and geometry of the boundary of pseudoconvex domains

Takeo Ohsawa. "∂̅-cohomology and geometry of the boundary of pseudoconvex domains." Annales Polonici Mathematici 91.2-3 (2007): 249-262. <http://eudml.org/doc/280645>.

@article{TakeoOhsawa2007,
abstract = {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.},
author = {Takeo Ohsawa},
journal = {Annales Polonici Mathematici},
keywords = {Levi-flat; Kähler manifold; plurisubharmonic exhaustion function; Hartogs type extension theorem; foliation},
language = {eng},
number = {2-3},
pages = {249-262},
title = {∂̅-cohomology and geometry of the boundary of pseudoconvex domains},
url = {http://eudml.org/doc/280645},
volume = {91},
year = {2007},
}

TY - JOUR
AU - Takeo Ohsawa
TI - ∂̅-cohomology and geometry of the boundary of pseudoconvex domains
JO - Annales Polonici Mathematici
PY - 2007
VL - 91
IS - 2-3
SP - 249
EP - 262
AB - 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.
LA - eng
KW - Levi-flat; Kähler manifold; plurisubharmonic exhaustion function; Hartogs type extension theorem; foliation
UR - http://eudml.org/doc/280645
ER -