Abstract
Let V be an asymptotically cylindrical Kahler manifold with asymptotic cross-section \(\mathfrak{D}\). Let (\(E_{\mathfrak{D}},\phi_{\mathfrak{D}}\)) be a stable Higgs bundle over \(\mathfrak{D}\), and (E, ε) a Higgs bundle over V which is asymptotic to (\(E_{\mathfrak{D}},\phi_{\mathfrak{D}}\)). In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant projectively Hermitian Yang-Mills metric on (E,ε).
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Acknowledgements
The author would like to express his deep gratitude to Dr. Thomas Walpuski for many conversations about their paper, as well as to the referees for their valuable comments.
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The author was partially supported by NSF in China (Grant Nos. 11625106, 11571332 and 11721101)
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Zhang, P. Hermitian Yang-Mills Metrics on Higgs Bundles over Asymptotically Cylindrical Kähler Manifolds. Acta. Math. Sin.-English Ser. 35, 1128–1142 (2019). https://doi.org/10.1007/s10114-019-8220-0
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DOI: https://doi.org/10.1007/s10114-019-8220-0