Hermitian Yang–Mills Metrics on Higgs Bundles over Asymptotically Cylindrical K?hler Manifolds

Let V be an asymptotically cylindrical K?hler manifold with asymptotic cross-section ■.Let ■ be a stable Higgs bundle over ■, and(E, φ) a Higgs bundle over V which is asymptotic to ■. 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, φ).