Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity II -- on Stein manifolds

Abstract

In this article, we consider Bergman kernels related to modules at boundary points on Stein manifolds, and obtain a log-subharmonicity property of the Bergman kernels. As applications, we obtain a lower estimate of weighted $L^2$ integrals on Stein manifolds, and reprove an effectiveness result of strong openness property of modules at boundary points on Stein manifolds.

arXiv comment21 pages, some typos are corrected. An appendix is add to show an example for explaining the results we obtain in the present paper