Zero Problems of the Bergman Kernel Function on the First Type of Cartan-Hartogs Domain*

Citation:

Xin ZHAO.Zero Problems of the Bergman Kernel Function on the First Type of Cartan-Hartogs Domain*[J].Chinese Annals of Mathematics B,2022,43(2):265~280
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Authors:

Xin ZHAO;

Foundation:

National Natural Science Foundation of China (No. 11871044) and the Natural Science Foundation of Hebei Province (No. A2019106037).
Abstract: The authors give the condition that the Bergman kernel function on the first type of Cartan-Hartogs domain exists zeros. If the Bergman kernel function of this type of domain has zeros, the zero set is composed of several path-connected branches, and there exists a continuous curve to connect any two points in the non-zero set.

Keywords:

Cartan-Hartogs domain, Zeros of Bergman kernel function, Path connectivity

Classification:

32A07, 32A25
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