Work

Uniqueness and Stability of Monge--Ampère Potentials in Big Cohomology Classes

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.00810

Authors: Dang, Quang-Tuan, Zhang, Lei, Zhou, Bin

Institutions: Peking University, Tsinghua University

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Tsinghua University

Award: G2538611429

OpenAlex ID: W7206189081

Cites: 6

Cited by: 1

Related to: 10