Existence of Hermitian-Einstein metrics is shown for analytically stable Higgs bundles over non-compact non-Kähler Hermitian manifolds under stated assumptions on the base.
Mochizuki, Kobayashi-Hitchin correspondence for tame har monic bundles and an application, Ast´ erisque,309, Soc
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Analytically stable Higgs bundles on some non-K\"ahler manifolds
Existence of Hermitian-Einstein metrics is shown for analytically stable Higgs bundles over non-compact non-Kähler Hermitian manifolds under stated assumptions on the base.