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

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.

Funding

National Outstanding Youth Science Fund Project of National Natural Science Foundation of China(11825101); National Key R &D Program of China(2021YFA1003100)