Kobayashi-Hitchin correspondence for analytically stable bundles

Takuro Mochizuki

Published 2017-12-25Version 1

We prove the existence of a Hermitian-Einstein metric on holomorphic vector bundles with a Hermitian metric satisfying the analytic stability condition, under some assumption for the underlying K\"ahler manifolds. We also study the curvature decay of the Hermitian-Einstein metrics. It is useful for the study of the classification of instantons and monopoles on the quotient of $4$-dimensional Euclidean space by some types of closed subgroups.