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Monge—Ampère Type Equations on Almost Hermitian Manifolds

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Abstract

In this paper we consider the Monge–Ampère type equations on compact almost Hermitian manifolds. We derive C∞ a priori estimates under the existence of an admissible \(\cal{C}\)-subsolution. Finally, we obtain an existence result if there exists an admissible supersolution.

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Acknowledgements

The author wish to thank his thesis advisor professor Xi Zhang for his constant encouragements. The author also thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P. R. China

    Jiao Gen Zhang

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  1. Jiao Gen Zhang
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Correspondence to Jiao Gen Zhang.

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Supported by the project “Analysis and Geometry on Bundle” of Ministry of Science and Technology of the People’s Republic of China (Grant No. SQ2020YFA070080) and by China Postdoctoral Science Foundation (Grant No. 290612)

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Zhang, J.G. Monge—Ampère Type Equations on Almost Hermitian Manifolds. Acta. Math. Sin.-English Ser. 39, 749–772 (2023). https://doi.org/10.1007/s10114-022-0394-1

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  • DOI: https://doi.org/10.1007/s10114-022-0394-1

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