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Transactions of the American Mathematical Society

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Higgs bundles over non-compact Gauduchon manifolds


Authors: Chuanjing Zhang, Pan Zhang and Xi Zhang
Journal: Trans. Amer. Math. Soc. 374 (2021), 3735-3759
MSC (2020): Primary 53C07, 14J60, 32Q15
DOI: https://doi.org/10.1090/tran/8323
Published electronically: January 21, 2021
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Abstract: In this paper, we prove a generalized Donaldson-Uhlenbeck-Yau theorem on Higgs bundles over a class of non-compact Gauduchon manifolds.


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Additional Information

Chuanjing Zhang
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China
Email: chjzhang@mail.ustc.edu.cn

Pan Zhang
Affiliation: School of Mathematical Sciences, Anhui University, Anhui 230601, People’s Republic of China
Email: panzhang20100@ahu.edu.cn

Xi Zhang
Affiliation: School of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, People’s Republic of China
Email: mathzx@ustc.edu.cn

DOI: https://doi.org/10.1090/tran/8323
Keywords: Higgs bundles, Gauduchon manifold, approximate Hermitian-Einstein structure, Hermitian-Einstein metric, non-compact
Received by editor(s): April 30, 2018
Received by editor(s) in revised form: July 16, 2018, August 9, 2020, and October 13, 2020
Published electronically: January 21, 2021
Additional Notes: The first author and the second author are both co-first authors, the third author is the corresponding author. The authors were partially supported by NSF in China No.11625106, 11801535 and 11721101. The first author was also supported by the China Postdoctoral Science Foundation (No.2018M642515) and the Fundamental Research Funds for the Central Universities. The second author was supported by the Natural Science Foundation of Universities of Anhui Province. The research was partially supported by the project “Analysis and Geometry on Bundle” of Ministry of Science and Technology of the People’s Republic of China, No. SQ2020YFA070080.
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