2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112816The 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-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 pagesComplex VariablesPrimary 32H15; Secondary 32F07;32F15text