Quantitative stability for the complex Monge-Amp\`ere equations I
Complex Variables
2024-05-29 v1 Analysis of PDEs
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.
Cite
@article{arxiv.2405.17491,
title = {Quantitative stability for the complex Monge-Amp\`ere equations I},
author = {Hoang-Son Do and Duc-Viet Vu},
journal= {arXiv preprint arXiv:2405.17491},
year = {2024}
}
Comments
Part I of arXiv:2209.00248, to appear in Analysis & PDE