Convergence Properties of the Yang-Mills Flow on Kaehler Surfaces

G. Daskalopoulos and R. Wentworth

We prove that the Yang-Mills flow on a Kaehler surface converges, in an appropriate sense which takes into account bubbling phenomena, to the double dual of the graded sheaf associated to the Harder-Narasimhan-Seshadri filtration of the initial holomorphic bundle. This generalizes to Kaehler surfaces the known result on Riemann surfaces and proves, in this case, a conjecture of Bando and Siu.