The Minimal Surfaces Over the Slanted Half-Planes, Vertical Strips and Single Slit

Abstract

In this chapter, 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. The content of this chapter is a shorter version of an article of the author’s report of 2011 and published in arXiv (http://arxiv.org/pdf/1204.2890.pdf) in 2012.