On $L^\infty$ estimates for complex Monge-Amp\`ere equations

Bin Guo; Duong H. Phong; Freid Tong

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On $L^\infty$ estimates for complex Monge-Amp\`ere equations

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arxiv 2106.02224 v1 pith:T7TZ2TYT submitted 2021-06-04 math.DG math.AP

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

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abstract

A PDE proof is provided for the sharp $L^\infty$ estimates for the complex Monge-Amp\`ere equation which 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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