In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near bou...We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.展开更多
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...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.展开更多
文摘In this paper, we give an explicit formula of the Bergman kernel function on Hua Construction of the second type when the parameters 1/p1,…, 1/pr-1 are positive integers and 1/pr is an arbitrary positive real number.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10171068) the Natural Science Foundation of Beijing (Grant No. 1012004).
文摘We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.
基金partially supported by the National Natural Science Foundation of China(Grant No.10471097)
文摘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.
