Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds
Complex Variables
2021-07-06 v1 Differential Geometry
Abstract
We develop a new approach to -a priori estimates for degenerate complex Monge-Amp\`ere equations on complex manifolds. It only relies on compactness and envelopes properties of quasi-plurisubharmonic functions. In a prequel \cite{GL21a} we have shown how this method allows one to obtain new and efficient proofs of several fundamental results in K\"ahler geometry. In \cite{GL21b} we have studied the behavior of Monge-Amp\`ere volumes on hermitian manifolds. We extend here the techniques of \cite{GL21a} to the hermitian setting and use the bounds established in \cite{GL21b}, producing new relative a priori estimates, as well as several existence results for degenerate complex Monge-Amp\`ere equations on compact hermitian manifolds.
Keywords
Cite
@article{arxiv.2107.01938,
title = {Quasi-plurisubharmonic envelopes 3: Solving Monge-Amp\`ere equations on hermitian manifolds},
author = {Vincent Guedj and Chinh H. Lu},
journal= {arXiv preprint arXiv:2107.01938},
year = {2021}
}