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arXiv · 2106.02224

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

Bin Guo·Duong H. Phong·Freid Tong
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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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Bin Guo, Duong H. Phong, Freid Tong. 2021-06-04. On $L^\infty$ estimates for complex Monge-Amp\`ere equations. https://arxiv.org/abs/2106.02224

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