Weighted pluripotential theory on complex K\"{a}hler manifolds

TL;DR

This paper extends pluripotential theory on complex Kähler manifolds by introducing weighted Green functions, exploring their properties, and generalizing Siciak's H-principle, thus advancing the theoretical framework in complex geometry.

Contribution

It develops a weighted pluripotential theory on Kähler manifolds, defining weighted Green functions and generalizing key principles like Siciak's H-principle.

Findings

Defined weighted pluricomplex Green functions.

Analyzed properties under holomorphic maps.

Generalized Siciak's H-principle.

Abstract

We introduce a weighted version of the pluripotential theory on complex K\"{a}hler 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.