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In the following article we study the limiting properties of the Yang-Millsflow associated to a holomorphic vector bundle E over an arbitrary compactK\"ahler manifold (X,{\omega}). In particular we show that the flow isdetermined at infinity by the holomorphic structure of E. Namely, if we fix anintegrable unitary reference connection A_0 defining the holomorphic structure,then the Yang-Mills flow with initial condition A_0, converges (away from anappropriately defined singular set) in the sense of the Uhlenbeck compactnesstheorem to a holomorphic vector bundle E_{\infty}, which is isomorphic to theassociated graded object of the Harder-Narasimhan-Seshadri filtration of(E,A_0). Moreover, E_{\infty} extends as a reflexive sheaf over the singularset as the double dual of the associated graded object. This is an extension ofprevious work in the cases of 1 and 2 complex dimensions and proves the generalcase of a conjecture of Bando and Siu.

Asymptotics of the Yang-Mills Flow for Holomorphic Vector Bundles Over K\"ahler Manifolds: The Canonical Structure of the Limit