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Injective hyperbolicity of domains. (English) Zbl 0847.32027
Let $$K_D$$ denote the Kobayashi-Royden pseudometric on a domain $$D$$ in $$\mathbb{C}^n$$, and let $$S_D$$ denote the pseudometric defined by K. T. Hahn [Ann. Pol. Math. 39, 71-81 (1981; Zbl 0476.32031)] using injective holomorphic mappings. In contrast to the situation for $$n = 1$$ where $$K_D = S_D$$ if and only if $$D$$ is simply connected, the author proves that for $$n \geq 3$$ the pseudometrics $$K_D$$ and $$S_D$$ always coincide.

##### MSC:
 32F45 Invariant metrics and pseudodistances in several complex variables
##### Keywords:
Hahn pseudometric; Kobayashi-Royden pseudometric
Zbl 0476.32031
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