The Limit of the Yang-Mills-Higgs Flow for twisted Higgs pairs

In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over Kähler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan–eshadri filtration of the initial twisted Higgs bundle.