Abstract
Let $\Omega$ be a smoothly bounded pseudoconvex domain in $\mathbb{C}^{n}$ and let $z_{0} \in b\Omega$ be a point of finite type. We also assume that the Levi form of $b\Omega$ is comparable in a neighborhood of $z_{0}$. Then we get a quantity which bounds from above and below the Bergman metric, Caratheodory metric and Kobayashi metric in a small constant and large constant sense.
Citation
Sanghyun Cho. "Estimates of invariant metrics on pseudoconvex domains with comparable Levi form." J. Math. Kyoto Univ. 42 (2) 337 - 349, 2002. https://doi.org/10.1215/kjm/1250283875
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