Note examines conditions for extending harmonic mappings quasiconformally, suggesting significant implications for their applications.
This note examines sufficient conditions for the quasiconformal extendibility of harmonic mappings defined in the unit disk. It is demonstrated that a harmonic strongly starlike mapping admits a quasiconformal extension to the entire plane, and an explicit formulation of its extension function is provided. Additionally, the quasiconformal extendibility of harmonic mappings defined in the exterior of the unit disk is explored.
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Xiu-Shuang Ma (2025) studied this question.
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