Journal
MATHEMATICA SCANDINAVICA
Volume 127, Issue 3, Pages 527-543Publisher
MATEMATISK INST
DOI: 10.7146/math.scand.a-128968
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Funding
- NNSF of China [11971124, 11901090]
- Department of Education of Guangdong Province, China [2018KQNCX285]
- NSF of Hunan [2020JJ6038]
- Scientific Research Fund of Hunan Provincial Education Department [20A070]
- Science and Technology Plan Project of Hunan Province [2016TP1020]
- Application-Oriented Characterized Disciplines, Double First-Class University Project of Hunan Province [Xiangjiaotong [2018]469]
- NSF of Guangdong Province [2021A1515010326]
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A uniformly continuous identification between the inner boundary of Omega and the Gromov boundary with a visual metric is shown, leading to boundary continuity for both quasiconformal homeomorphisms and rough quasi-isometries between domains equipped with quasihyperbolic metrics.
Let Omega subset of R-n be a Gromov hyperbolic, phi-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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