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

TL;DR

This paper investigates the properties of Bergman kernels associated with modules at boundary points on Stein manifolds, establishing log-subharmonicity and deriving applications for $L^2$ estimates and module openness.

Contribution

It introduces a log-subharmonicity property of Bergman kernels on Stein manifolds and applies it to estimate integrals and prove openness results.

Findings

Log-subharmonicity of Bergman kernels at boundary points

Lower bounds for weighted $L^2$ integrals on Stein manifolds

Reproof of strong openness property for modules at boundary points

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.