Hartogs type extension theorems on some domains in Kähler manifolds

Takeo Ohsawa. "Hartogs type extension theorems on some domains in Kähler manifolds." Annales Polonici Mathematici 106.1 (2012): 243-254. <http://eudml.org/doc/281083>.

@article{TakeoOhsawa2012,
abstract = {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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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.},
author = {Takeo Ohsawa},
journal = {Annales Polonici Mathematici},
keywords = {analytic continuation; Hartogs' extension; Kähler manifold; Levi form; cohomology},
language = {eng},
number = {1},
pages = {243-254},
title = {Hartogs type extension theorems on some domains in Kähler manifolds},
url = {http://eudml.org/doc/281083},
volume = {106},
year = {2012},
}

TY - JOUR
AU - Takeo Ohsawa
TI - Hartogs type extension theorems on some domains in Kähler manifolds
JO - Annales Polonici Mathematici
PY - 2012
VL - 106
IS - 1
SP - 243
EP - 254
AB - 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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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.
LA - eng
KW - analytic continuation; Hartogs' extension; Kähler manifold; Levi form; cohomology
UR - http://eudml.org/doc/281083
ER -