On $L^\infty$ estimates for Monge-Amp\`ere and Hessian equations on nef classes
Differential Geometry
2024-03-13 v1 Analysis of PDEs
Abstract
The PDE approach developed earlier by the first three authors for 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.
Keywords
Cite
@article{arxiv.2111.14186,
title = {On $L^\infty$ estimates for Monge-Amp\`ere and Hessian equations on nef classes},
author = {Bin Guo and Duong H. Phong and Freid Tong and Chuwen Wang},
journal= {arXiv preprint arXiv:2111.14186},
year = {2024}
}