Lu Qi-Keng conjectue and Hua domain

Abstract

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 C n . 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-Kähler metrics, the equivalence between the Einstein-Kähler metric and the Bergman metric, etc.

Remarks on two theorems of Qi-Keng Lu

“…The lecture and survey article of Weiping Yin [13] is one of the motivations for us to write this article dedicated to Qi-Keng Lu. We are grateful to Siqi Fu for his kindness of communicating with us on the work of [11].…”