Fiberwise Bergman kernels, vector bundles, and log-subharmonicity

Abstract

In this article, we consider Bergman kernels related to modules at boundary points for singular hermitian metrics on holomorphic vector bundles, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted $L^2$ integrals on sublevel sets of plurisubharmonic functions, and reprove an effectiveness result of the strong openness property of the modules.

arXiv comment32 pages, all comments are welcome! arXiv admin note: substantial text overlap with arXiv:2205.08044, arXiv:2206.00443