  This is a sequel of our paper [arXiv:1809.08425] on the Quot-scheme limit and
variational properties of Donaldson's functional, which established its
coercivity for slope stable holomorphic vector bundles over smooth projective
varieties. Assuming that the coercivity is uniform in a certain sense, we
provide a new proof of the Donaldson-Uhlenbeck-Yau theorem, in such a way that
the analysis involved in the proof is elementary except for the asymptotic
expansion of the Bergman kernel.
