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.

21 pages, comments are welcome