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

Facultad de Ingeniería y Ciencias

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

20 Citas (Scopus)

Resumen

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.

Idioma original	Inglés
Páginas (desde-hasta)	53-59
Número de páginas	7
Publicación	Archiv der Mathematik
Volumen	104
N.º	1
DOI	https://doi.org/10.1007/s00013-014-0714-5
Estado	Publicada - ene 2014

Acceder al documento

10.1007/s00013-014-0714-5

Citar esto

@article{47cc5798188b4e0ba94a9c45c32a1ce1,

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",

volume = "104",

pages = "53--59",

journal = "Archiv der Mathematik",

issn = "0003-889X",

publisher = "Springer International Publishing",

number = "1",

}

TY - JOUR

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

AU - Hernández, Rodrigo

AU - Martín, María J.

PY - 2014/1

Y1 - 2014/1

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

AN - SCOPUS:84925482269

SN - 0003-889X

VL - 104

SP - 53

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

Resumen

Acceder al documento

Huella

Citar esto