Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

Rodrigo Hernández; María J. Martín

doi:10.1007/s00013-014-0714-5

Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

Rodrigo Hernández
, María J. Martín

Faculty of Engineering and Science

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

18 Scopus citations

Abstract

We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.

Original language	English
Pages (from-to)	53-59
Number of pages	7
Journal	Archiv der Mathematik
Volume	104
Issue number	1
DOIs	https://doi.org/10.1007/s00013-014-0714-5
State	Published - Jan 2014

Keywords

Harmonic mapping
Quasiconformal extension
Schwarzian derivative
Univalence criterion

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10.1007/s00013-014-0714-5

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title = "Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative",

abstract = "We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.",

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

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

note = "Publisher Copyright: {\textcopyright} 2014, Springer Basel.",

year = "2014",

month = jan,

doi = "10.1007/s00013-014-0714-5",

language = "English",

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T1 - Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

AU - Hernández, Rodrigo

AU - Martín, María J.

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N2 - We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.

AB - We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.

KW - Harmonic mapping

KW - Quasiconformal extension

KW - Schwarzian derivative

KW - Univalence criterion

UR - https://www.scopus.com/pages/publications/84925482269

U2 - 10.1007/s00013-014-0714-5

DO - 10.1007/s00013-014-0714-5

M3 - Article

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SN - 0003-889X

VL - 104

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EP - 59

JO - Archiv der Mathematik

JF - Archiv der Mathematik

IS - 1

ER -

Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative

Abstract

Keywords

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