Uniform $L^\infty$ estimates: subsolutions to fully nonlinear partial differential equations

Bin Guo; Duong H. Phong

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Uniform $L^\infty$ estimates: subsolutions to fully nonlinear partial differential equations

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arxiv 2401.11572 v1 pith:3P4EDVW5 submitted 2024-01-21 math.AP math.DG

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

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keywords estimatesuniformdifferentialequationsfullypartialadvantageahler

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abstract

Uniform bounds are obtained using the auxiliary Monge-Amp\`ere equation method for solutions of very general classes of fully non-linear partial differential equations, assuming the existence of a ${C}$-subsolution in the sense of G. Sz\'ekelyhidi and B. Guan. The main advantage over previous estimates is in the K\"ahler case, where the new estimates remain uniform as the background metric is allowed to degenerate.

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