Stability estimates for the complex Monge-Amp\`ere and Hessian equations

Bin Guo; Duong H. Phong; Freid Tong

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Stability estimates for the complex Monge-Amp\`ere and Hessian equations

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arxiv 2106.03913 v1 pith:22HBRK24 submitted 2021-06-07 math.DG math.AP

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

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keywords equationsestimateshessianmonge-ampstabilitycasecomplexdegenerations

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A new proof for stability estimates for the complex Monge-Amp\`ere and Hessian equations is given, which does not require pluripotential theory. A major advantage is that the resulting stability estimates are then uniform under general degenerations of the background metric in the case of the Monge-Amp\`ere equation, and under degenerations to a big class in the case of Hessian equations.

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