Annales Academi� Scientiarum Fennic�
Mathematica
Volumen 38, 2013, 617-630

QUASICONFORMAL EXTENSION OF HARMONIC MAPPINGS IN THE PLANE

Rodrigo Hern�ndez and Mar�a J. Mart�n

Universidad Adolfo Ib��ez, Facultad de Ingenier�a y Ciencias
Av. Padre Hurtado 750, Vi�a del Mar, Chile; rodrigo.hernandez 'at' uai.cl

Universidad Aut�noma de Madrid, Departamento de Matem�ticas
28049 Madrid, Spain; mariaj.martin 'at' uam.es

Abstract. Let f be a sense-preserving harmonic mapping in the unit disk. We give a sufficient condition in terms of the pre-Schwarzian derivative of f to ensure that it can be extended to a quasiconformal map in the complex plane.

2010 Mathematics Subject Classification: Primary 30C45, 30C55.

Key words: Pre-Schwarzian derivative, quasiconformal extension, harmonic mapping.

Reference to this article: R. Hern�ndez and M.J. Mart�n: Quasiconformal extension of harmonic mappings in the plane. Ann. Acad. Sci. Fenn. Math. 38 (2013), 617-630.

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doi:10.5186/aasfm.2013.3824