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

Shijie Bao; Qi'an Guan

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

Complex Variables 2023-01-03 v2

Authors: Shijie Bao , Qi'an Guan

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.

Keywords

Bergman kernel log-subharmonicity Stein manifolds modules at boundary points weighted L2 integrals strong openness property

Cite

@article{arxiv.2205.08044,
  title  = {Modules at boundary points, fiberwise Bergman kernels, and log-subharmonicity II -- on Stein manifolds},
  author = {Shijie Bao and Qi'an Guan},
  journal= {arXiv preprint arXiv:2205.08044},
  year   = {2023}
}

Comments

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

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