On $L^\infty$ estimates for complex Monge-Ampère equations

Bin Guo; Duong Phong; Freid Tong

doi:10.4007/annals.2023.198.1.4

July 2023 On $L^\infty$ estimates for complex Monge-Ampère equations

Bin Guo, Duong Phong, Freid Tong

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Abstract

A PDE proof is provided for the sharp $L^\infty$ estimates for the complex Monge-Ampère equation that had required pluripotential theory before. The proof covers both cases of fixed background as well as degenerating background metrics. It extends to more general fully non-linear equations satisfying a structural condition, and it also gives estimates of Trudinger type.

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Bin Guo, Duong Phong, and Freid Tong "On $L^\infty$ estimates for complex Monge-Ampère equations," Annals of Mathematics 198(1), 393-418, (July 2023). https://doi.org/10.4007/annals.2023.198.1.4

Published: July 2023

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