Teichmüller’s Problem for Gromov Hyperbolic Domains

Qingshan Zhou, Antti Rasila*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 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 languageEnglish
JournalIsrael Journal of Mathematics
DOIs
StateE-pub ahead of print - 9 Sep 2022

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