A Demailly-type approximation of singular Finsler metrics

We establish a Demailly-type approximation theorem for singular Finsler metrics satisfying the multiple coarse $L^p$ extension property on holomorphic vector bundles. As an application, we obtain a new proof of the fact that the multiple coarse $L^p$ extension property characterizes Griffiths positivity, as shown by Deng–Wang–Zhang–Zhou.