GENERALIZED JOHN GROMOV HYPERBOLIC DOMAINS AND EXTENSIONS OF MAPS

Qingshan Zhou; Liulan Li; Antti Rasila

doi:10.7146/math.scand.a-128968

GENERALIZED JOHN GROMOV HYPERBOLIC DOMAINS AND EXTENSIONS OF MAPS

Qingshan Zhou, Liulan Li, Antti Rasila

Mathematics with Computer Science

Research output: Contribution to journal › Article › peer-review

2 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 language	English
Pages (from-to)	527-543
Number of pages	17
Journal	Mathematica Scandinavica
Volume	127
Issue number	3
DOIs	https://doi.org/10.7146/math.scand.a-128968 https://doi.org/10.7146/math.scand.a-128968
State	Published - 2021

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title = "GENERALIZED JOHN GROMOV HYPERBOLIC DOMAINS AND EXTENSIONS OF MAPS",

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.",

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AU - Li, Liulan

AU - Rasila, Antti

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N2 - 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.

AB - 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.

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DO - 10.7146/math.scand.a-128968

M3 - 文章

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EP - 543

JO - Mathematica Scandinavica

JF - Mathematica Scandinavica

IS - 3

ER -

GENERALIZED JOHN GROMOV HYPERBOLIC DOMAINS AND EXTENSIONS OF MAPS

Abstract

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