Yang-Mills-Higgs Limits of Reflexive Higgs Sheaves

For stable Higgs bundles, Hermitian-Einstein metrics can be obtained as limits of the Yang-Mills-Higgs (Y-M-H) flow. We study the algebraic structure of subsequential limits of this flow for reflexive Higgs sheaves over compact Kähler manifolds, without assuming stability. We prove that the limiting reflexive Higgs sheaf is isomorphic to the double dual of the graded sheaf associated with the Harder-Narasimhan-Seshadri filtration of the initial sheaf.