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Planar harmonic univalent and related mappings. (English) Zbl 1099.31001

This is an expository article describing a wide range of results on harmonic univalent and related mappings in the unit disk, including the special classes of harmonic functions that are starlike, convex, multivalent or meromorphic. It complements the book of P. L. Duren [Harmonic mappings in the plane, Cambridge University Press (2004; Zbl 1055.31001)].

MSC:

31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
30C20 Conformal mappings of special domains
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C55 General theory of univalent and multivalent functions of one complex variable
44A15 Special integral transforms (Legendre, Hilbert, etc.)

Citations:

Zbl 1055.31001
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