PreprintCC BY 4.0arXiv
Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes
Abstract
In this paper, we establish a stability estimate and a uniform estimate for the modulus of continuity of solutions to the degenerate complex Monge-Ampère equation in big cohomology classes. Consequently, we prove the uniqueness of solutions to complex Monge-Ampère mean field equations for a sufficiently small parameter.
Related
- Uniqueness and sharp boundary estimates for degenerate Monge-Ampère equations with singular measures
- Mumford--Morita--Miller classes in generalised cohomology theories
- On the Cohomology Classes of Certain Eisenstein-Kronecker Forms
- Big and nef cohomology classes on compact Kähler spaces
- Realizability of Cohomology Classes in Orthogonal Grassmannians
BibTeX
@misc{dang2026uniqueness,
title = {{Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes}},
author = {Quang-Tuan Dang and Lei Zhang and Bin Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00810},
eprint = {2609.00810},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00810},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes
AU - Quang-Tuan Dang
AU - Lei Zhang
AU - Bin Zhou
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00810
UR - https://arxiv.org/abs/2609.00810
AB - In this paper, we establish a stability estimate and a uniform estimate for the modulus of continuity of solutions to the degenerate complex Monge-Ampère equation in big cohomology classes. Consequently, we prove the uniqueness of solutions to complex Monge-Ampère mean field equations for a sufficiently small parameter.
ER -