Teichmüller’s Problem for Gromov Hyperbolic Domains

Qingshan Zhou; Antti Rasila

doi:10.1007/s11856-022-2352-0

Teichmüller’s Problem for Gromov Hyperbolic Domains

Qingshan Zhou, Antti Rasila^*

^*Corresponding author for this work

Mathematics with Computer Science

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

7 Scopus citations

Abstract

Let TK(D) be the class of K-quasiconformal automorphisms of a domain D ⊂ ℝn with identity boundary values. Teichmüller’s problem is to determine how far a given point x ∈ D can be mapped under a mapping f∈ TK(D). We estimate this distance between x and f(x) from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichmüller’s problem for Gromov hyperbolic domains in ℝn with identity values at the boundary of infinity. As applications, we obtain results on Teichmüller’s problem for ψ-uniform domains and inner uniform domains in ℝn.

Original language	English
Journal	Israel Journal of Mathematics
DOIs	https://doi.org/10.1007/s11856-022-2352-0
State	E-pub ahead of print - 9 Sep 2022

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title = "Teichm{\"u}ller{\textquoteright}s Problem for Gromov Hyperbolic Domains",

abstract = "Let TK(D) be the class of K-quasiconformal automorphisms of a domain D ⊂ ℝn with identity boundary values. Teichm{\"u}ller{\textquoteright}s problem is to determine how far a given point x ∈ D can be mapped under a mapping f∈ TK(D). We estimate this distance between x and f(x) from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichm{\"u}ller{\textquoteright}s problem for Gromov hyperbolic domains in ℝn with identity values at the boundary of infinity. As applications, we obtain results on Teichm{\"u}ller{\textquoteright}s problem for ψ-uniform domains and inner uniform domains in ℝn.",

author = "Qingshan Zhou and Antti Rasila",

year = "2022",

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doi = "10.1007/s11856-022-2352-0",

language = "英语",

journal = "Israel Journal of Mathematics",

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T1 - Teichmüller’s Problem for Gromov Hyperbolic Domains

AU - Zhou, Qingshan

AU - Rasila, Antti

PY - 2022/9/9

Y1 - 2022/9/9

N2 - Let TK(D) be the class of K-quasiconformal automorphisms of a domain D ⊂ ℝn with identity boundary values. Teichmüller’s problem is to determine how far a given point x ∈ D can be mapped under a mapping f∈ TK(D). We estimate this distance between x and f(x) from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichmüller’s problem for Gromov hyperbolic domains in ℝn with identity values at the boundary of infinity. As applications, we obtain results on Teichmüller’s problem for ψ-uniform domains and inner uniform domains in ℝn.

AB - Let TK(D) be the class of K-quasiconformal automorphisms of a domain D ⊂ ℝn with identity boundary values. Teichmüller’s problem is to determine how far a given point x ∈ D can be mapped under a mapping f∈ TK(D). We estimate this distance between x and f(x) from the above by using two different metrics, the distance ratio metric and the quasihyperbolic metric. We study Teichmüller’s problem for Gromov hyperbolic domains in ℝn with identity values at the boundary of infinity. As applications, we obtain results on Teichmüller’s problem for ψ-uniform domains and inner uniform domains in ℝn.

U2 - 10.1007/s11856-022-2352-0

DO - 10.1007/s11856-022-2352-0

M3 - 文章

SN - 0021-2172

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Teichmüller’s Problem for Gromov Hyperbolic Domains

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