The minimal surfaces over the slanted half-planes, vertical strips and   single slit
  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. 
Liulan Li, S. Ponnusamy and M. Vuorinen
math.CV