Harmonic Mappings in the Plane

By Peter L. Duren. 2004

722 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6eadc44b2de0a7f3f126e5a1913abf59cc1191f6

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In Applied Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Landau and Bloch theorems for harmonic mappings (2006, background): “For a recent account of the theory of univalent harmonic mappings we refer the reader to the very interesting book of Duren 4 .”
Planar harmonic univalent and related mappings. (2005, background): “Since there are several survey articles and books ([21], [23], [24], [27], [49]) on harmonic mappings and related areas, we present only a selection of the results relevant to our precise objective.”
Variability regions for certain families of harmonic univalent mappings (2013, background): “Thus, we may sometimes restrict our attention to the subclass S0H 1⁄4 f f2SH : fzð0Þ 1⁄4 0g: Clearly, S(S0H(SH: Although both SH and S0H are known to be normal families, only S0H is compact with respect to the topology of locally uniform convergence [3,4].”
Associate and conjugate minimal immersions in MxR (2005, background): “Observe that in case where KM = 0 the result can be encountered in [ 4 ], see the theorem in Section 10.2.”
Improved Bohr’s inequality for locally univalent harmonic mappings (2017, background): “P. Duren, Harmonic mappings in the plane, Cambridge University Press, Cambridge, 2004.”
On Harmonic Quasiconformal Quasi-Isometries (2007, background): “ore these mappings are notanalytic. Intensive studies during the past two decades show that much of the classical function theory can be generalized to harmonic mappings (see the recent book of Duren [9] and the survey of Bshouty and Hengartner [7]). The purpose of this paper is to continue the stud”
Some properties of a class of elliptic partial differential operators (2014, background): “For α = 0, there are numerous discussions on coefficient estimates of harmonic mappings in the literature, see for example [7, 8, 9, 11, 13, 17, 24].”
Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings (2011, background): “One of the beautiful results of Clunie and Sheilsmall [5] (see also [8]) shows that f is univalent in D and its range f (D) is CHD if”
The Schwarzian derivative for harmonic mappings (2003, background): “The general harmonic shear of a conformal mapping' convex in the horizontal direction, with dilatation ! = q 2 , has the form f = h +g, where h g = ' and g 0 = q 2 h 0 . (See [1] or [ 2 ].) Solving the pair of linear equations, one finds h 0 = ' 0 /(1 q 2 ). A calculation then”