Quantitative stability for the complex Monge-Ampere equations

We prove several quantitative stability estimates for solutions of complex Monge-Ampere equations when both the cohomology class and the prescribed singularity vary. In a broad sense, our results fit well into the study of degeneration of families of Kaehler-Einstein metrics. The key mechanism in ou...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2022-11
Main Authors: Hoang-Son Do, Duc-Viet Vu
Format: Article
Language:English
Subjects:
Degeneration
Homology
Mathematical analysis
Stability
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove several quantitative stability estimates for solutions of complex Monge-Ampere equations when both the cohomology class and the prescribed singularity vary. In a broad sense, our results fit well into the study of degeneration of families of Kaehler-Einstein metrics. The key mechanism in our method is the pluripotential theory in the space of potentials of finite lower energy.
ISSN:2331-8422