Gromov hyperbolicity of the 𝑗_{𝐺} and 𝚥̃_{𝐺} metrics

Hästö, Peter

doi:10.1090/S0002-9939-05-08053-6

Gromov hyperbolicity of the $j_G$ and ${\tilde \jmath }_G$ metrics
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by Peter A. Hästö

Proc. Amer. Math. Soc. 134 (2006), 1137-1142

DOI: https://doi.org/10.1090/S0002-9939-05-08053-6

Published electronically: August 29, 2005

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Abstract:

In this note it is shown that the ${\tilde \jmath }_G$ metric is always Gromov hyperbolic, but that the $j_G$ metric is Gromov hyperbolic if and only if $G$ has exactly one boundary point. As a corollary we get a new proof for the fact that the quasihyperbolic metric is Gromov hyperbolic in uniform domains.

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