Zero problems of the Bergman kernel function on the second type of Cartan-Hartogs domain

Abstract

We give the condition that the Bergman kernel function of the second type of Cartan-Hartogs domain has zeros. When the Bergman kernel function of this type of domain has zeros, the topological properties of the zero cluster are proved, and the conditions are given to judge whether a boundary point on the definition domain of the Bergman kernel function is an aggregation point of the zero cluster.

Keywords:

• Cartan-Hartogs domain
• zeros of Bergman kernel function
• path connectivity
• aggregation point

AMS Subject Classifications:

• 32A07
• 32A25

Acknowledgments

The authors thank the referees for many valuable comments and suggests.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research supported by National Natural Science Foundation of China [grant number 11871044].