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Harmonic deformability of planar curves

Eleutherius Symeonidis (2021)

Commentationes Mathematicae Universitatis Carolinae

We study the formerly established concept of deformation of a planar curve and clarify its applicability and range. We present several applications on classical curves.

Harmonic mappings onto parallel slit domains

Michael Dorff, Maria Nowak, Magdalena Wołoszkiewicz (2011)

Annales Polonici Mathematici

We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.

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