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Gromov hyperbolicity of the $j_G$ and ${\tilde \jmath }_G$ metrics
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 …