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The Dirichlet Problem on Almost Hermitian Manifolds

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Abstract

We prove second-order a priori estimate on the boundary for the Dirichlet problem of a class of fully nonlinear equations on compact almost Hermitian manifolds with smooth boundary. As applications, we solve the Dirichlet problem of the Monge–Ampère type equation and of the degenerate Monge–Ampère equation.

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Acknowledgements

The first named author would like to thank his advisor Professor Gang Tian for helpful suggestions, constant encouragement, and support. The second named author thanks Professor Jean-Pierre Demailly, Valentino Tosatti, and Ben Weinkove for invaluable directions. The authors are also grateful to the anonymous referees and the editor for their careful reading and helpful suggestions which greatly improved the paper.

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Authors and Affiliations

  1. Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Chang Li

  2. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Tao Zheng

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  1. Chang Li
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  2. Tao Zheng
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Correspondence to Tao Zheng.

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Chang Li: Supported by the China post-doctoral Grant No. BX20200356. Tao Zheng: Supported by Beijing Institute of Technology Research Fund Program for Young Scholars.

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Li, C., Zheng, T. The Dirichlet Problem on Almost Hermitian Manifolds. J Geom Anal 31, 6452–6480 (2021). https://doi.org/10.1007/s12220-020-00540-w

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