Lu Qi-Keng's Problem

Abstract

This expository article, intended to be accessible to students, surveys results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in C^n. Six open problems are stated. The article is based on a lecture at the third Korean several complex variables symposium held at the Global Analysis Research Center at Seoul National University in December 1998.

14 pages; to appear in the Journal of the Korean Mathematical Society

Cited by in corpus (11)

• Automorphisms of normal quasi-circular domains
• On the $p-$Bergman theory
• Rigidity theorem by the minimal point of the Bergman kernel
• The Bergman kernel of a certain Hartogs domain and the polylogarithm function
• On the Bergman Projection and the Lu Qi-Keng Conjecture
• Lu Qi-Keng Conjectue and Hua Domain
• The Bergman kernel of the symmetrized polydisc in higher dimensions has zeros
• Proper holomorphic mappings, Bells formula and the Lu Qi-Keng problem on tetrablock
• Vanishing Bergman kernels on the disk
• Lu Qi-Keng's problem for intersection of two complex ellipsoids
• Weighted Bergman kernel functions associated to meromorphic functions