Log-hyperconvexity index and Bergman kernel

Published 21 Jun 2022 in math.CV | (2206.10133v1)

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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