Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 1065–1308
Issue 4, 805–1064
Issue 3, 549–803
Issue 2, 279–548
Issue 1, 1–278

Volume 17, 10 issues

Volume 16, 10 issues

Volume 15, 8 issues

Volume 14, 8 issues

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1948-206X (online)
ISSN 2157-5045 (print)
 
Author index
To appear
 
Other MSP journals
Quantitative stability for complex Monge–Ampère equations, I

Hoang-Son Do and Duc-Viet Vu
Vol. 18 (2025), No. 5, 1271–1308
DOI: 10.2140/apde.2025.18.1271
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.

Keywords
Monge–Ampère equation, convex weights, lower energy, non-pluripolar products
Mathematical Subject Classification
Primary: 32Q15, 32U15
Milestones
Received: 22 September 2023
Revised: 18 February 2024
Accepted: 29 March 2024
Published: 10 May 2025
Authors
Hoang-Son Do
Institute of Mathematics
Vietnam Academy of Science and Technology
Hanoi
Vietnam
Duc-Viet Vu
Department of Mathematics and Computer Sciences
University of Cologne
Cologne
Germany
© 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

Open Access made possible by participating institutions via Subscribe to Open.