Quasiconformal Extensions of Harmonic Univalent Mappings of the Unit Disk
Xiu-Shuang Ma
TL;DR
This paper establishes conditions under which harmonic univalent mappings of the unit disk can be extended quasiconformally to the entire plane, providing explicit extension formulas and exploring exterior domain cases.
Contribution
It offers new sufficient conditions for quasiconformal extendibility of harmonic mappings and explicit formulas for their extensions.
Findings
Strongly starlike harmonic mappings admit quasiconformal extensions.
Explicit extension functions are derived.
Extension criteria are explored for mappings outside the unit disk.
Abstract
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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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Algebraic and Geometric Analysis