English

Log-hyperconvexity index and Bergman kernel

Complex Variables 2022-09-23 v1

Abstract

We obtain a quantitative estimate of Bergman distance when ΩCn\Omega \subset \mathbb{C}^n is a bounded domain with log-hyperconvexity index αl(Ω)>n1+(n1)(n+3)2\alpha_l(\Omega)>\frac{n-1+\sqrt{(n-1)(n+3)}}{2}, as well as the A2(logA)qA^2(\log A)^q-integrability of the Bergman kernel KΩ(,w)K_{\Omega}(\cdot, w) when αl(Ω)>0\alpha_l(\Omega)>0.

Keywords

Cite

@article{arxiv.2206.10133,
  title  = {Log-hyperconvexity index and Bergman kernel},
  author = {Bo-Yong Chen and Zhiyuan Zheng},
  journal= {arXiv preprint arXiv:2206.10133},
  year   = {2022}
}
R2 v1 2026-06-24T11:58:00.631Z