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We study the Yang-Mills flow on a holomorphic vector bundle E over a compactKahler manifold X. We construct a natural barrier function along the flow, andintroduce some techniques to study the blow-up of the curvature along the flow.Making some technical assumptions, we show how our techniques can be used toprove that the curvature of the evolved connection is uniformly bounded awayfrom an analytic subvariety determined by the Harder-Narasimhan-Seshadrifiltration of E. We also discuss how our assumptions are related to stabilityin some simple cases.

Remarks on the Yang-Mills flow on a compact Kahler manifold