Quantitative stability for the complex Monge-Ampère equations I

Abstract

We generalize several known stability estimates for complex Monge-Ampère equations to the setting of low (or high) energy potentials. We apply our estimates to obtain, among other things, a quantitative domination principle, and metric properties of the space of potentials of finite energy. Further applications will be given in subsequent papers.

Part I of arXiv:2209.00248, to appear in Analysis & PDE