Acta Mathematica Sinica, English Series

, Volume 35, Issue 7, pp 1128–1142 | Cite as

Hermitian Yang-Mills Metrics on Higgs Bundles over Asymptotically Cylindrical Kähler Manifolds

  • Pan ZhangEmail author


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).


Higgs bundles asymptotically cylindrical Kähler manifolds Hermitian Yang-Mills metrics 

MR(2010) Subject Classification

53C07 14J60 32Q15 


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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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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of MathematicsSun Yat-sen UniversityGuangzhouP. R. China

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