The minimal surfaces over the slanted half-planes, vertical strips and single slit

TL;DR

This paper explicitly derives the representation of minimal surfaces and harmonic mappings over slanted half-planes, vertical strips, and single slit regions, providing visual illustrations using Mathematica.

Contribution

It introduces explicit formulas for minimal surfaces over specific complex domains and visualizes these mappings, advancing understanding of harmonic mappings in geometric function theory.

Findings

Explicit representations of minimal surfaces over the specified domains

Harmonic mappings corresponding to these minimal surfaces

Visual illustrations of the mappings and surfaces

Abstract

In this paper, we discuss the minimal surfaces over the slanted half-planes, vertical strips, and single slit whose slit lies on the negative real axis. The representation of these minimal surfaces and the corresponding harmonic mappings are obtained explicitly. Finally, we illustrate the harmonic mappings of each of these cases together with their minimal surfaces pictorially with the help of mathematica.