Weighted pluripotential theory on complex Kähler manifolds

Abstract

We introduce a weighted version of the pluripotential theory on complex Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behaviour under holomorphic maps. We also establish a generalization of Siciak's H-principle.

arXiv commentCorrected proof of the domination principle, some notation uniformized, new references added