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

Ahuja, Om P.

JIPAM, J. Inequal. Pure Appl. Math. 6, No. 4, Paper No. 122, 18 p. (2005).

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)].

Reviewer: D. A. Brannan (Milton Keynes)

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.)

Keywords:

harmonic mapping; univalent function; multivalent function; meromorphic function

Citations:

Zbl 1055.31001