Comparison between the Kobayashi and Carathéodory distances on strongly pseudoconvex bounded domains in 𝐶ⁿ

Venturini, Sergio

doi:10.1090/S0002-9939-1989-0984819-X

Comparison between the Kobayashi and Carathéodory distances on strongly pseudoconvex bounded domains in $\textbf {C}^ n$
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by Sergio Venturini

Proc. Amer. Math. Soc. 107 (1989), 725-730

DOI: https://doi.org/10.1090/S0002-9939-1989-0984819-X

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Abstract:

In this paper we prove that the ratio between the Carathéodory distance and the Kobayashi distance in a strongly pseudoconvex bounded domain in ${{\mathbf {C}}^n}$ is arbitrarily close to 1 whenever at least one of the points is sufficiently near the boundary.

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