Lu Qi-Keng conjectue and Hua domain

The first part of this paper discusses the motivation for the Lu Qi-Keng conjecture and the results about the presence or the absence of zeroes of the Bergman kernel function of a bounded domain in ℂn. Its second part summarizes the main results on the Hua domains, such as the explicit Bergman kernel function, the comparison theorem for the invariant metrics, the explicit complete Einstein-Kahler metrics, the equivalence between the Einstein-Kahler metric and the Bergman metric, etc.