Uniform entropy and energy bounds for fully non-linear equations

Bin Guo; Duong H. Phong

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Uniform entropy and energy bounds for fully non-linear equations

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arxiv 2207.08983 v1 pith:7YI5TI3C submitted 2022-07-18 math.DG math.APmath.CV

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

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keywords boundsuniformenergyequationequationsfullynon-linearalexandrov-bakelman-pucci

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abstract

Energy bounds which are uniform in the background metric are obtained from upper bounds for entropy-like quantities. The argument is based on auxiliary Monge-Amp\`ere equations involving sublevel sets, and bypasses the Alexandrov-Bakelman-Pucci maximum principle. In particular, it implies uniform $L^\infty$ bounds for systems coupling a fully non-linear equation to its linearization, generalizing the cscK equation.

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