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Teichmüller displacement theorem on Gromov hyperbolic spaces
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 67 / Issue 4 / November 2024
- Published online by Cambridge University Press:
- 06 November 2024, pp. 1148-1166
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Given a Gromov hyperbolic domain
$G\subsetneq \mathbb{R}^n$ with uniformly perfect Gromov boundary, Zhou and Rasila recently proved that for all quasiconformal homeomorphisms 
$\psi\colon G\to G$ with identity value on the Gromov boundary, the quasihyperbolic displacement 
$k_G(x,\psi(x))$ for all 
$x\in G$ 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.
