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Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds

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Abstract

We establish second order estimates for a general class of fully nonlinear elliptic equations with gradient terms on almost Hermitian manifolds including the deformed Hermitian-Yang-Mills equation and the equation in the proof of Gauduchon conjecture by Székelyhidi-Tosatti-Weinkove. As applications, we also consider the existence of Monge-Ampère  equation and Hessian equations.

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Notes

  1. From now on, the C below denotes the constants those may change from line to line, and it doesn’t depend on D that we yet to choose.

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Acknowledgements

We are very grateful to Professor Xi Zhang for countless advice. We would like to thank Jianchun Chu for generous discussions. We are also grateful to Rirong Yuan for his helpful suggestions. The first author was partially supported by China Postdoctoral Science Foundation 2021M700127 and 2022T150584. The second author is partially supported by the China Postdoctoral Science Foundation 2022M713057. The authors would like to thank the referees for many useful suggestions and comments.

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Authors and Affiliations

  1. Westlake Institute for Advanced Study (Westlake University), 18 Shilongshan Road, Cloud Town, Xihu District, Hangzhou, People’s Republic of China

    Liding Huang

  2. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China

    Jiaogen Zhang

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  1. Liding Huang
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Huang, L., Zhang, J. Fully nonlinear elliptic equations with gradient terms on compact almost Hermitian manifolds. Math. Z. 303, 36 (2023). https://doi.org/10.1007/s00209-022-03202-5

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