Monge-Amp\`ere operators on compact K\"ahler manifolds
Complex Variables
2007-05-23 v2 Analysis of PDEs
Abstract
We study the complex Monge-Amp\` ere operator on compact K\"ahler manifolds. We give a complete description of its range on the set of plurisubharmonic functions with gradient and finite self energy, generalizing to this compact setting results of U.Cegrell from the local pluripoltential theory. We give some applications to complex dynamics and to the existence of K\"ahler-Einstein metrics on singular manifolds.
Keywords
Cite
@article{arxiv.math/0504234,
title = {Monge-Amp\`ere operators on compact K\"ahler manifolds},
author = {Vincent Guedj and Ahmed Zeriahi},
journal= {arXiv preprint arXiv:math/0504234},
year = {2007}
}
Comments
29 pages, We show how to extend the results of the previous version to arbitrary dimension and indicate some applications