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Curvature estimates for a class of Hessian quotient type curvature equations

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Abstract

In this paper, we are concerned with the hypersurface that can be locally represented as a graph and satisfies a class of Hessian quotient type curvature equations. We establish interior curvature estimates under the condition of \(0\le l<k\le C_{n-1}^{p-1}\). As an application, we prove Bernstein type theorem for this type curvature equation. We also focus on closed star shaped hypersurface satisfying this type curvature equation and obtain the global curvature estimation.

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  1. School of Mathematics and Statistics, Fuyang Normal University, Fuyang, 236037, Anhui, People’s Republic of China

    Jundong Zhou

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Communicated by A. Mondino.

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Research of the authors was supported by the Natural Science Foundation of AnhuiProvince Education Department (No. KJ2021A0659, KJ2021A0661, 2022AH051320 and 2022AH051322); University Excellent Young Talents Research Project of Anhui Province (No. gxyq2022039) and Doctoral Scientific Research Initiation Project of Fuyang Normal University (No. 2021KYQD0011).

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Zhou, J. Curvature estimates for a class of Hessian quotient type curvature equations. Calc. Var. 63, 88 (2024). https://doi.org/10.1007/s00526-024-02703-x

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