Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings

Rodrigo Hernández; María J. Martín

doi:10.1007/s12220-013-9413-x

Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings

Rodrigo Hernández
, María J. Martín

Facultad de Ingeniería y Ciencias

Producción científica: Contribución a una revista › Artículo › revisión exhaustiva

61 Citas (Scopus)

Resumen

In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation ω_f of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.

Idioma original	Inglés
Páginas (desde-hasta)	64-91
Número de páginas	28
Publicación	Journal of Geometric Analysis
Volumen	25
N.º	1
DOI	https://doi.org/10.1007/s12220-013-9413-x
Estado	Publicada - ene 2013

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title = "Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings",

abstract = "In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation ωf of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.",

keywords = "Becker{\textquoteright}s criterion, Convexity, Harmonic mappings, Pre-Schwarzian derivative, Schwarzian derivative, Univalence",

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

note = "Publisher Copyright: {\textcopyright} 2013, Mathematica Josephina, Inc.",

year = "2013",

month = jan,

doi = "10.1007/s12220-013-9413-x",

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N2 - In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation ωf of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.

AB - In this paper we introduce a definition of the pre-Schwarzian and the Schwarzian derivatives of any locally univalent harmonic mapping f in the complex plane without assuming any additional condition on the (second complex) dilatation ωf of f. Using the new definition for the Schwarzian derivative of harmonic mappings, we prove theorems analogous to those by Chuaqui, Duren, and Osgood. Also, we obtain a Becker-type criterion for the univalence of harmonic mappings.

KW - Becker’s criterion

KW - Convexity

KW - Harmonic mappings

KW - Pre-Schwarzian derivative

KW - Schwarzian derivative

KW - Univalence

UR - https://www.scopus.com/pages/publications/84875925457

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JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

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Pre-Schwarzian and Schwarzian Derivatives of Harmonic Mappings

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