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Abstract Given a Gromov hyperbolic domain G Rⁿ with uniformly perfect Gromov boundary, Zhou and Rasila recently proved that for all quasiconformal homeomorphisms G G with identity value on the Gromov boundary, the quasihyperbolic displacement kG (x, (x) ) for all x G is bounded above. In this paper, we generalize this result and establish Teichmüller displacement theorem for quasi-isometries of Gromov hyperbolic spaces in a quantitative way. As applications, we obtain its connections to bilipschitz extensions of certain Gromov hyperbolic spaces.
Zhou et al. (Fri,) studied this question.