On L∞ estimates for Monge–Ampère and Hessian equations on nef classes

The PDE approach developed earlier by the first three authors for $L^{\infty }$ estimates for fully nonlinear equations on Kähler manifolds is shown to apply as well to Monge–Ampère and Hessian equations on nef classes. In particular, one obtains a new proof of the estimates of Boucksom, Eyssidieux, Guedj and Zeriahi (2010) and Fu, Guo and Song (2020) for the Monge–Ampère equation, together with their generalization to Hessian equations.