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Canonical Metrics on Holomorphic Filtrations over Compact Hermitian Manifolds

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Abstract

The purpose of this paper is twofold. We first solve the Dirichlet problem for \(\tau \)-Hermitian–Einstein equations on holomorphic filtrations over compact Hermitian manifolds. Secondly, by using Uhlenbeck–Yau’s continuity method, we prove the existence of approximate \(\tau \)-Hermitian–Einstein structure on holomorphic filtrations over closed Gauduchon manifolds.

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Acknowledgements

Pan Zhang is supported by the Fundamental Research Funds for the Central Universities (No. 19lgpy239).

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Authors and Affiliations

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

    Zhenghan Shen

  2. School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People’s Republic of China

    Pan Zhang

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  1. Zhenghan Shen
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  2. Pan Zhang
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Correspondence to Pan Zhang.

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Shen, Z., Zhang, P. Canonical Metrics on Holomorphic Filtrations over Compact Hermitian Manifolds. Commun. Math. Stat. 8, 219–237 (2020). https://doi.org/10.1007/s40304-019-00199-y

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  • DOI: https://doi.org/10.1007/s40304-019-00199-y

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