Shear Construction Of Certain Harmonic Univalent Functions And Weierstrass-Enneper Representation - Ahmad El-Faqeer, Ahmad Sulaiman (2023)
Geometric function theory is an intriguing field of study because harmonic maps and the minimal surfaces are connected and also it is used in many other fields. The major part of this thesis consists of several original results on harmonic functions and their minimal surface connections. Initially, we present two generalized harmonic univalent functions using the shearing construction, determine a horizontal convexity criterion for these generalized univalent harmonic mappings, and look into the directional convexity and univalency of special subclasses of harmonic mapping convolutions.