Quasiconformal Extensions of Harmonic Univalent Mappings of the Interior and Exterior Unit Disk

Abstract: In this note, we consider the sufficient coefficient condition for some harmonic mappings in the unit disk which can be extended to the whole complex plane. As an application of this result, we will prove that a harmonic strongly starlike mapping has a quasiconformal extension to the whole plane and will give an explicit form of its extension function. We also investigate the quasiconformal extension of harmonic mappings in the exterior unit disk.