Curvature Currents and Chern Forms of Singular Hermitian Metrics on Holomorphic Vector Bundles

Abstract

We study curvature currents of singular Hermitian metrics on holomorphic vector bundles. It is known that curvature currents of singular Hermitian metrics on vector bundles are generally not defined with measure coefficients. In this paper, we give some sufficient conditions that curvature currents can be defined with measure coefficients. Moreover, we investigate Chern forms associated with singular Hermitian metrics.