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 It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-19,
author = {Takeo Ohsawa},
title = {Hartogs type extension theorems on some domains in K\"ahler manifolds},
journal = {Annales Polonici Mathematici},
volume = {105},
year = {2012},
pages = {243-254},
zbl = {1262.32013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-19}
}
Takeo Ohsawa. Hartogs type extension theorems on some domains in Kähler manifolds. Annales Polonici Mathematici, Tome 105 (2012) pp. 243-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap106-0-19/