QUASICONFORMAL MAPS WITH THIN DILATATIONS

Christopher J. Bishop

doi:10.5565/PUBLMAT6622207

QUASICONFORMAL MAPS WITH THIN DILATATIONS

Christopher J. Bishop

Mathematics

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

Abstract

We give an estimate that quantifies the fact that a normalized quasiconformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author’s quasiconformal folding method for constructing entire functions; in particular an application to constructing transcendental wandering domains given by Fagella, Godillon, and Jarque [7].

Original language	English
Pages (from-to)	715-727
Number of pages	13
Journal	Publicacions Matematiques
Volume	66
DOIs	https://doi.org/10.5565/PUBLMAT6622207
State	Published - 2022

Keywords

conformal modulus
holomorphic dynamics
Pompeiu’s formula
quasiconformal folding
quasiconformal maps

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10.5565/PUBLMAT6622207

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abstract = "We give an estimate that quantifies the fact that a normalized quasiconformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author{\textquoteright}s quasiconformal folding method for constructing entire functions; in particular an application to constructing transcendental wandering domains given by Fagella, Godillon, and Jarque [7].",

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AB - We give an estimate that quantifies the fact that a normalized quasiconformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author’s quasiconformal folding method for constructing entire functions; in particular an application to constructing transcendental wandering domains given by Fagella, Godillon, and Jarque [7].

KW - conformal modulus

KW - holomorphic dynamics

KW - Pompeiu’s formula

KW - quasiconformal folding

KW - quasiconformal maps

UR - https://www.scopus.com/pages/publications/85133382164

U2 - 10.5565/PUBLMAT6622207

DO - 10.5565/PUBLMAT6622207

M3 - Article

AN - SCOPUS:85133382164

SN - 0214-1493

VL - 66

SP - 715

EP - 727

JO - Publicacions Matematiques

JF - Publicacions Matematiques

ER -

QUASICONFORMAL MAPS WITH THIN DILATATIONS

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Keywords

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