On $L^\infty$ estimates for Monge-Amp\`ere and Hessian equations on nef classes

Bin Guo; Chuwen Wang; Duong H. Phong; Freid Tong

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On $L^\infty$ estimates for Monge-Amp\`ere and Hessian equations on nef classes

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arxiv 2111.14186 v1 pith:7RKQ7QQH submitted 2021-11-28 math.DG math.AP

Bin Guo , Duong H. Phong , Freid Tong , Chuwen Wang This is my paper · ORCID

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abstract

The PDE approach developed earlier by the first three authors for $L^\infty$ estimates for fully non-linear equations on K\"ahler manifolds is shown to apply as well to Monge-Amp\`ere and Hessian equations on nef classes. In particular, one obtains a new proof of the estimates of Boucksom-Eyssidieux-Guedj-Zeriahi and Fu-Guo-Song for the Monge-Amp\`ere equation, together with their generalization to Hessian equations.

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