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arXiv · 2206.10133

Log-hyperconvexity index and Bergman kernel

Bo-Yong Chen·Zhiyuan Zheng
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Abstract

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

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Bo-Yong Chen, Zhiyuan Zheng. 2022-06-21. Log-hyperconvexity index and Bergman kernel. https://arxiv.org/abs/2206.10133

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