The results of Donaldson and Uhlenbeck-Yau have since been extended by other authors. Uhlenbeck and Yau's article is important in giving a clear reason that stability of the holomorphic vector bundle can be related to the analytic methods used in constructing a hermitian Yang-Mills connection. The essential mechanism is that if an approximating sequence of hermitian connections fails to converge to the required Yang-Mills connection, then they can be rescaled to converge to a subsheaf which can be verified to be destabilizing by Chern-Weil theory.