We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-7,
author = {Maritza M. Branker and Ma\l gorzata Stawiska},
title = {Weighted pluripotential theory on compact K\"ahler manifolds},
journal = {Annales Polonici Mathematici},
volume = {95},
year = {2009},
pages = {163-177},
zbl = {1166.32020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-7}
}
Maritza M. Branker; Małgorzata Stawiska. Weighted pluripotential theory on compact Kähler manifolds. Annales Polonici Mathematici, Tome 95 (2009) pp. 163-177. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap95-2-7/