Lu Qi-Keng Conjectue and Hua Domain

Details Lu Qi-Keng Conjectue and Hua Domain Lu Qi-Keng Conjectue and Hua Domain

2006-05-16

arxiv.org/abs/math/0605428v2

Mathematics

Complex Variables

Dedicated to Lu Qi-Keng on the occasion of his 80th birthday, 16 pages

Scientific paper

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 ${\bf{C^n}}$. 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-K\"ahler metrics, the equivalence between the Einstein-K\"ahler metric and the Bergman metric etc.

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