Generalized John Gromov hyperbolic domains and extensions of maps


  • Qingshan Zhou
  • Liulan Li
  • Antti Rasila



Let $\Omega \subset \mathbb{R}^n$ be a Gromov hyperbolic, $\varphi$-length John domain. We show that there is a uniformly continuous identification between the inner boundary of $\Omega$ and the Gromov boundary endowed with a visual metric, By using this result, we prove the boundary continuity not only for quasiconformal homeomorphisms, but also for more generally rough quasi-isometries between the domains equipped with the quasihyperbolic metrics.


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How to Cite

Zhou, Q., Li, L., & Rasila, A. (2021). Generalized John Gromov hyperbolic domains and extensions of maps. MATHEMATICA SCANDINAVICA, 127(3).