Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds
Differential Geometry
2009-03-24 v3
Abstract
We prove the existence and uniqueness of the solutions of some very general type of degenerate complex Monge-Amp\`ere equations. This type of equations is precisely what is needed in order to construct K\"ahler-Einstein metrics over irreducible singular K\"ahler spaces with ample or trivial canonical sheaf and singular K\"ahler-Einstein metrics over varieties of general type.
Cite
@article{arxiv.0710.5109,
title = {Degenerate complex Monge-Amp\`ere equations over compact K\"ahler manifolds},
author = {Jean-Pierre Demailly and Nefton Pali},
journal= {arXiv preprint arXiv:0710.5109},
year = {2009}
}
Comments
The present manuscript expands and completes a paper accepted for publication in the International Journal of Mathematics, which had to be shortened in view of the length of the manuscript and of the demands of referees - in particular it gives more details about the relation with the existing litterature (see Appendix C)