Quantitative stability for the complex Monge-Amp\`ere equations I

TL;DR

This paper extends stability estimates for complex Monge-Ampère equations to potentials with varying energy levels, enabling new quantitative and metric insights into the space of finite energy potentials.

Contribution

It generalizes known stability estimates to low and high energy potentials, providing new quantitative domination principles and metric properties.

Findings

Established stability estimates for a broader class of potentials.

Derived a quantitative domination principle.

Analyzed metric properties of the space of finite energy potentials.

Abstract

We generalize several known stability estimates for complex Monge-Amp\`ere 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.