Semi-stable Higgs sheaves and Bogomolov type inequality
  In this paper, we study semistable Higgs sheaves over compact K\"ahler manifolds, we prove that there is an approximate admissible Hermitian-Einstein structure on a semi-stable reflexive Higgs sheaf and consequently, the Bogomolove type inequality holds on a semi-stable reflexive Higgs sheaf. 
Jiayu Li, Chuanjing Zhang, Xi Zhang
math.DG