Harmonic shears of elliptic integrals

DOI10.1216/rmjm/1181069741zbMath1087.31005OpenAlexW1969876195MaRDI QIDQ2566504

Jan Szynal, Michael Dorff

Publication date: 26 September 2005

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181069741

zbMATH Keywords

minimal surfaceharmonic mappingelliptic integralharmonic shearWeierstrass-Enneper formula

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Harmonic, subharmonic, superharmonic functions on other spaces (31C05) Elliptic functions and integrals (33E05)

Related Items (7)

Harmonic shears of slit and polygonal mappings ⋮ A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM ⋮ A family of minimal surfaces and univalent planar harmonic mappings ⋮ Minimal surfaces over stars ⋮ Unnamed Item ⋮ Harmonic Univalent Mappings and Minimal Graphs ⋮ A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM II

Cites Work

• The global theory of doubly periodic minimal surfaces
• Some existence and uniqueness theorems for doubly periodic minimal surfaces
• Minimal surfaces of least total curvature and moduli spaces of plane polygonal arcs
• Boundary values versus dilatations of harmonic mappings
• Classification of doubly-periodic minimal surfaces of genus zero
• Harmonic shears of regular polygons by hypergeometric functions
• Harmonic univalent functions
• Harmonic mappings related to Scherk's saddle-tower minimal surfaces
• Growth, distortion and coefficient bounds for plane harmonic mappings convex in one direction
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