GENERALIZED JOHN GROMOV HYPERBOLIC DOMAINS AND EXTENSIONS OF MAPS

Qingshan Zhou, Liulan Li, Antti Rasila

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Let Ω ⊂ ℝn be a Gromov hyperbolic, φ-length John domain. We show that there is a uniformly continuous identification between the inner boundary of Ω 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.

Original languageEnglish
Pages (from-to)527-543
Number of pages17
JournalMathematica Scandinavica
Volume127
Issue number3
DOIs
StatePublished - 2021

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