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arXiv · 2112.02354

On the modulus of continuity of solutions to complex Monge-Amp\`ere equations

Bin Guo·Duong H. Phong·Freid Tong·Chuwen Wang
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Abstract

In this paper, we prove a uniform and sharp estimate for the modulus of continuity of solutions to complex Monge-Amp\`ere equations, using the PDE-based approach developed by the first three authors in their approach to supremum estimates for fully non-linear equations in K\"ahler geometry. As an application, we derive a uniform diameter bound for K\"ahler metrics satisfying certain Monge-Amp\`ere equations.

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Bin Guo, Duong H. Phong, Freid Tong, Chuwen Wang. 2021-12-04. On the modulus of continuity of solutions to complex Monge-Amp\`ere equations. https://arxiv.org/abs/2112.02354

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