Lu Qi-Keng Conjectue and Hua Domain
arXiv:math/0605428
Abstract
The first part I talk about the motivation for Lu Qi-Keng conjecture and the results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in . The second part I summarize the main results on Hua domains, such as the explicit Bergman kernel function, comparison theorem for the invariant metrics, explicit complete Einstein-Kähler metrics, the equivalence between the Einstein-Kähler metric and the Bergman metric etc.
Dedicated to Lu Qi-Keng on the occasion of his 80th birthday, 16 pages