The Hermitian-Yang-Mills Iteration on Stable Bundles

In this paper, based on recent results for the prescribed Hermitian-Yang-Mills (HYM) tensor and its twisted variants by Fan-Wang-Yang-Yau, we provide a dynamical construction of Hermitian-Einstein metrics on stable holomorphic vector bundles and its extension to Higgs bundles. Additionally, in the appendix, we use the heat flow method to give a new proof of the existence and uniqueness of solutions to the twisted prescribed HYM tensor equation, as well as its generalization to Higgs bundles.