Estimates of invariant metrics on pseudoconvex domains of finite type in \(\mathbb{C}^3\). (English) Zbl 1474.32034

Summary: Let \(\Omega\) be a smoothly bounded pseudoconvex domain in \(\mathbb{C}^3\) and assume that \(z_0 \in b \Omega\) is a point of finite 1-type in the sense of D’Angelo. Then, there are an admissible curve \(\Gamma \subset \Omega \cup \{z_0 \}\), connecting points \(q_0 \in \Omega\) and \(z_0 \in b \Omega\), and a quantity \(M(z, X)\), along \(z \in \Gamma\), which bounds from above and below the Bergman, Caratheodory, and Kobayashi metrics in a small constant and large constant sense.


32F45 Invariant metrics and pseudodistances in several complex variables
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