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Original Article

Modules at Boundary Points, Fiberwise Bergman Kernels, and Log-Subharmonicity

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
School of Mathematical Sciences, Peking University, Beijing 100871, China

Shijie Bao and Qi’an Guan contributed equally to this work.

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Abstract

In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which implies a concavity property related to the Bergman kernels. As applications, we reprove the sharp effectiveness result related to a conjecture posed by Jonsson–Mustaţă and the effectiveness result of strong openness property of the modules at boundary points.

Keywords

Bergman kernelsL2 extensionStrong openness property

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Peking Mathematical Journal
Volume 7 Issue 2,
September 2024
Pages 441-470
DOI: 10.1007/s42543-023-00070-8

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Cite this article:
Bao, S., Guan, Q. Modules at Boundary Points, Fiberwise Bergman Kernels, and Log-Subharmonicity. Peking Math J 7, 441-470 (2024). https://doi.org/10.1007/s42543-023-00070-8

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Received: 10 October 2022
Revised: 02 March 2023
Accepted: 18 March 2023
Published: 03 May 2023
© Peking University 2023