Lu Qi-Keng's Problem
Harold P. Boas (Texas A&M University)
TL;DR
This paper surveys the current knowledge and open problems regarding the zeros of the Bergman kernel function in bounded domains in complex space, aiming to be accessible to students.
Contribution
It provides an accessible survey of known results and open problems about the zeros of the Bergman kernel function in several complex variables.
Findings
Summary of known results on Bergman kernel zeros
Presentation of six open problems in the field
Educational overview for students and researchers
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.
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Taxonomy
TopicsMeromorphic and Entire Functions · Holomorphic and Operator Theory · Algebraic and Geometric Analysis