Canonical metrics on holomorphic quiver bundles over compact generalized Kahler manifolds

The purpose of this paper is twofold. By introducing the (alpha, sigma, tau)-Hermite-Yang-Mills flow, we first solve the Dirichlet problem for (alpha, sigma, tau)-Hermite-Yang-Mills equations on holomorphic quiver bundles over compact generalized Kahler manifolds. Second, by using Uhlenbeck-Yau's continuity method, we prove that the (alpha, sigma, tau)-semi-stability implies the existence of approximate (alpha, sigma, tau)-Hermite-Yang-Mills structure on holomorphic quiver bundles over compact generalized K & auml;hler manifolds.