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Continuous Solutions to Complex Hessian Equations on Hermitian Manifolds

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Abstract

In this paper, we study and discuss existence and continuity of solution to complex Hessian equation \((\chi + dd^c \cdot )^k\wedge \omega ^{n-k}=cf\omega ^n\) on Hermitian manifold \((X,\omega )\), where \(\chi \) is some smooth real \((1,1)-\)form in X and Hermitian form \(\omega \) satisfies that at every given point on X, there exist a local chart \(\Omega \) and a smooth real-valued function G such that \(e^{G}\omega \) is a Kähler form on \(\Omega .\)

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Acknowledgements

The authors would like to thank the referees very much for a very careful reading and valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Hanoi National University of Education, Hanoi, 100000, Vietnam

    Le Mau Hai

  2. Department of Mathematics, Hanoi Architectural University, Hanoi, 100000, Vietnam

    Vu Van Quan

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  1. Le Mau Hai
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  2. Vu Van Quan
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Correspondence to Vu Van Quan.

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Hai, L.M., Van Quan, V. Continuous Solutions to Complex Hessian Equations on Hermitian Manifolds. J Geom Anal 33, 368 (2023). https://doi.org/10.1007/s12220-023-01431-6

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