Twisted Higgs bundles over noncompact Gauduchon manifolds

Abstract

In this paper, we study the existence of canonical metrics on twisted Higgs bundles over a class of noncompact Gauduchon manifolds. When the twisted Higgs bundle is stable, we prove that there must exist a Hermitian-Einstein metric on it. When the twisted Higgs bundle is semi-stable, we prove that there is an approximate Hermitian-Einstein structure on it.