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.

Fiberwise Bergman kernels, vector bundles, and log-subharmonicity

“…In [1] (see also [2]), we considered Bergman kernels related to modules at boundary points of the sub-level sets, and obtained the log-subharmonicity property of the Bergman kernels. We applied the log-subharmonicity to get a lower estimate of weighted L 2 integrals on sublevel sets, and reproved the effectiveness result of strong openness property of modules at boundary points.…”