Lu Qi-Keng conjectue and Hua domain  

作　　者：YIN WeiPing 

机构地区：[1]School of Mathematical Sciences,Capital Normal University,Beijing 100037,China

出　　处：《Science China Mathematics》2008年第4期803-818,共16页中国科学：数学（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(Grant No.10471097)

摘　　要：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 ?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-K?hler metrics, the equivalence between the Einstein-K?hler metric and the Bergman metric, etc.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-K(?)hler metrics,the equivalence between the Einstein-K(?)hler metric and the Bergman metric,etc.

关 键 词：Lu Qi-Keng conjecture zeroes of the Bergman kernel function Hua domains Einstein-Kahler metric Bergman metric 

分 类 号：O186.1[理学—数学]