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The PDE approach developed earlier by the first three authors for L ∞ 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.
Guo et al. (Wed,) studied this question.