Title: Relative uniform estimates for complex Monge-Ampere type equations

Abstract: We proved a relative uniform estimate for a class of Monge-Ampere type equations on compact K\"ahler manifolds. It provides a unified approach to Trudinger-type estimates and uniform estimates, and the method can be applied to sharpen some previous results on the modulus of continuity of solutions, stability estimates, and estimates on Green's functions. The argument is based on the De Giorgi iteration for complex Monge-Ampere equations developed by Guo-Phong-Tong and the construction of appropriate comparison K\"ahler metrics.