A note on curvature estimate of the Hermitian-Yang-Mills flow
  In this paper, we study the curvature estimate of the Hermitian-Yang-Mills flow on holomorphic vector bundles. In one simple case, we show that the curvature of the evolved Hermitian metric is uniformly bounded away from the analytic subvariety determined by the Harder-Narasimhan-Seshadri filtration of the holomorphic vector bundle. 
Jiayu Li, Chuanjing Zhang and Xi Zhang
math.DG