Geometric properties of harmonic shears

DOI10.1007/BF03321057zbMath1056.30023MaRDI QIDQ1880504

Paul Greiner

Publication date: 28 September 2004

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

zbMATH Keywords

boundary behaviorharmonic mappingharmonic shear

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Geometric function theory (30C99) General theory of univalent and multivalent functions of one complex variable (30C55)

Related Items (17)

Harmonic shears of slit and polygonal mappings ⋮ Curvature properties of planar harmonic mappings ⋮ A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM ⋮ Harmonic shears of regular polygons by hypergeometric functions ⋮ Construction of planar harmonic functions ⋮ On directional convexity of harmonic mappings in the plane ⋮ Harmonic shears and numerical conformal mappings ⋮ Characterization of univalent harmonic mappings with integer or half-integer coefficients ⋮ Convex combinations of planar harmonic mappings realized through convolutions with half-strip mappings ⋮ Harmonic close-to-convex functions and minimal surfaces ⋮ Rotations of convex harmonic univalent mappings ⋮ Univalent harmonic mappings and lift to the minimal surfaces ⋮ Convolutions of harmonic mappings convex in one direction ⋮ Convolution properties of some harmonic mappings in the right half-plane ⋮ On the coefficient conjecture of Clunie and Sheil-Small on univalent harmonic mappings ⋮ CLASSIFICATION OF UNIVALENT HARMONIC MAPPINGS ON THE UNIT DISK WITH HALF-INTEGER COEFFICIENTS ⋮ A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM II

Uses Software

• Mathematica

Cites Work

• Boundary values versus dilatations of harmonic mappings
• Harmonic Mappings with Given Dilatation
• On the boundary behavior of orientation-preserving harmonic mappings
• Boundary correspondence and dilatation of harmonic mappings
• Planar Harmonic Maps with Inner and Blaschke Dilatations
• Harmonic univalent functions

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