非紧Gauduchon流形上的twisted Higgs丛

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 exists 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.