【摘要】
We prove a uniform estimate for the continuity of solutions to complex Monge--Ampère equations on compact Hermitian manifolds, using an auxiliary function method. As an application, we derive a uniform diameter bound for Hermitian metrics along the weak Chern--Ricci flow. Our approach also extends to the study of H\"older regularity of the least singular solution to the complex Monge--Ampère equation with a big reference form, as considered in [Boucksom, Guedj, Lu, Peking Math J (2025).]
