Bergman kernels over polarized Kähler manifolds, Bergman logarithmic flatness, and a question of Lu-Tian

Peter Ebenfelt, Ming Xiao, Hang Xu

Let $M$ be a complete Kähler manifold, and let $(L,h)\to M$ be a positive line bundle inducing a Kähler metric $g$ on $M$. We study two Bergman kernels in this setting: the Ber…