Ahlfors-Weill extensions for harmonic mappings

Iason Efraimidis; Rodrigo Hernández; María J. Martín

doi:10.1016/j.jmaa.2023.127053

Ahlfors-Weill extensions for harmonic mappings

Iason Efraimidis, Rodrigo Hernández, María J. Martín

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

Abstract

We provide two new formulas for quasiconformal extension to C‾ for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.

Original language	English
Article number	127053
Journal	Journal of Mathematical Analysis and Applications
Volume	523
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2023.127053
State	Published - 15 Jul 2023
Externally published	Yes

Keywords

Harmonic mapping
Quasiconformal extension
Schwarzian derivative

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10.1016/j.jmaa.2023.127053

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title = "Ahlfors-Weill extensions for harmonic mappings",

abstract = "We provide two new formulas for quasiconformal extension to C‾ for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.",

keywords = "Harmonic mapping, Quasiconformal extension, Schwarzian derivative",

author = "Iason Efraimidis and Rodrigo Hern{\'a}ndez and Mart{\'i}n, {Mar{\'i}a J.}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

year = "2023",

month = jul,

day = "15",

doi = "10.1016/j.jmaa.2023.127053",

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T1 - Ahlfors-Weill extensions for harmonic mappings

AU - Efraimidis, Iason

AU - Hernández, Rodrigo

AU - Martín, María J.

PY - 2023/7/15

Y1 - 2023/7/15

N2 - We provide two new formulas for quasiconformal extension to C‾ for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.

AB - We provide two new formulas for quasiconformal extension to C‾ for harmonic mappings defined in the unit disk and having sufficiently small Schwarzian derivative. Both are generalizations of the Ahlfors-Weill extension for holomorphic functions.

KW - Harmonic mapping

KW - Quasiconformal extension

KW - Schwarzian derivative

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U2 - 10.1016/j.jmaa.2023.127053

DO - 10.1016/j.jmaa.2023.127053

M3 - Article

AN - SCOPUS:85148752175

SN - 0022-247X

VL - 523

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 127053

ER -

Ahlfors-Weill extensions for harmonic mappings

Abstract

Keywords

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