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.}",

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KW - Quasiconformal extension

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KW - Univalence criterion

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

Abstract

Keywords

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