Covering stability of Bergman kernels on K\"ahler hyperbolic manifolds

Abstract

This paper is a sequel to \cite{Xu}. In this paper, an estimation of the Bergman Kernel of K\"ahler hyperbolic manifold is given by the $L^2$ estimate and the Bochner formula. As an application, an effective criterion of the very ampleness of the canonical line bundle of K\"ahler hyperbolic manifold is given, which is a generalization of Yeung's result.