Semi-stable quiver bundles over Gauduchon manifolds

Abstract

In this paper, we prove the existence of the approximate $ (\sigma, \tau) $-Hermitian Yang-Mills structure on the $ (\sigma, \tau) $-semi-stable quiver bundle $ \mathcal{R} = (\mathcal{E}, \phi) $ over compact Gauduchon manifolds. An interesting aspect of this work is that the argument on the weakly $ L^{2}_1 $-subbundles is different from [Álvarez-Cónsul and García-Prada, Comm. Math. Phys., 2003] and [Hu-Huang, J. Geom. Anal., 2020].

Keywords

• (σ，τ)-semi-stability
• approximate (σ，τ)-hermitian yang-mills structure
• continuity method